ion beam modification of metals: compositional and microstructural

Progress in Surface Science, Vol. 32, pp. 211-332 0079-6816/89 $0.00 + .50 Printed in the U.S.A. All rights reserved. Copyright © 1990 Pergamon Press plc

ION BEAM MODIFICATION OF METALS: COMPOSITIONAL AND MICROSTRUCTURAL CHANGES

G A R Y S. W A S

Departments of Nuclear Engineering and Materials Science and Engineering, University of Michigan, Ann Arbor, M148109

Abst rac t

Ion implantation has become a highly developed tool for modifying the structure and properties of metals and alloys. In addition to direct implantation, a variety of other ion beam techniques such as ion beam mixing, ion beam assisted deposition and plasma source ion implantation have been used increasingly in recent years. The modifications constitute composit ional and microstructural changes in the surface of the metal. This leads to alterations in physical propert ies (transport , optical, corrosion, oxidation), as well as mechanical properties (strength, hardness, wear resistance, fatigue resistance). The compositional changes brought about by ion bombardment are classified into recoil implantation, cascade mixing, rad ia t ion-enhanced dif fusion, rad ia t ion- induced segregat ion, Gibbsian adsorption and sputtering which combine to produce an often complicated compositional variation within the implanted layer and often, well beyond. Microstructurally, the phases present are often altered from what is expected from equilibrium thermodynamics giving rise to order- d i so rde r t r ans fo rma t ions , me ta s t ab l e ~ (c rys ta l l ine , amorphous or quasicrystalline) phase formation and growth, as well as densification, grain growth, formation of a preferred texture and the formation of a high density dislocation network. All these effects need to be understood before one can determine the effect of ion bombardment on the physical and mechanical properties of metals. This paper reviews the literature in terms of the compositional and microstructural changes induced by ion bombardment, whether by direct implantation, ion beam mixing or other forms of ion irradiation. The topics are introduced as well as reviewed, making this a more pedogogical approach as opposed to one which treats only recent developments. The aim is to provide the tools needed to understand the consequent changes in physical and mechanical properties.

211

212

1. Introduction

G.S. WAS

Contents

2. Ion Beam Modification Techniques

3. Compositional Changes

A. Recoil implantation B. Cascade mixing C. Chemical effects D. Radiation-enhanced diffusion E. Radiation-induced segregation E Gibbsian adsorption G. Sputtering H. Phenomenological model for surface composition changes I. Implant redistribution during ion implantation

4. Microstructural Changes

A. Phase stability B. Metastable phases C. Additional microstructural effects of ion implantation

5. Summary

References

Abbrev ia t i ons

AES bcc CSRO DM fcc GA hcp IBAD IBM PS PSII RED RIS TEM TSRO

Auger electron spectroscopy body centered cubic Chemical short range order Displacement mixing face centered cubic Gibbsian adsorption hexagonal close packed Ion beam assisted deposition Ion beam mixing Preferential sputtering Plasma source ion implantation Radiation enhanced diffusion Radiation-induced segregation Transmission electron microscopy Topological short range order

213

214

218

220 224 229 233 239 256 258 262 268

270

271 286 314

322

324

ION BEAM MODIFICATION OF METALS

1. Introduction

213

The use of ion beams for altering the properties of materials was pioneered in

the 1960s with the introduction of electrically active elements into silicon and

other semiconduct ing materials [1]. It became widely adopted by the

microelectronics industry in the 1970s and has developed into a well established

and precision industry [2]. The first application of ion implantation into metals

was reported in 1969 by Dearnaley [3] at the Harwell Laboratory, who

addressed the possibili ty of improving mechanical and corrosion behavior of

steels that are of relevance to the nuclear industry. Rapidly thereafter, the

attributes of ion implantation as a surface modification technique became

realized and activity in ion implantation of metals mushroomed.

In compar ison with al ternat ive surface modif ica t ion techniques , ion

implantation has a number of advantages: 1) the process is inherently low

temperature and thermal distortion of components is not a problem, 2) since ion

implantation is not a coating process, there is no interface that may become susceptible to decohesion due to mechanical stress or corrosion, 3) dimensional

changes are negligible on an engineering tolerance scale, being on the order of a

few tens of nanometers, 4) surface polish is improved due to preferential sputter

erosion of asperities, 5) the implanted atoms are dispersed on a microscopic (and

sometimes on an atomic) level producing the most efficient and beneficial effect

of the additive, and 6) significant compressive surface stresses are produced

which will partially compensate externally imposed tensile stresses and lengthen

component life against creep or fatigue failure by surface initiated cracking.

In addition to these practical attributes, a more general attribute of the

implantation process is that it is a non-equilibrium process. As a result the

implanted target may form non-equi l ibr ium or metas tab le phases or

microstructures. The study of these microstructures has generated a great deal

of interest with regard to the mechanical and physical properties they possess.

For example, the superior corrosion properties which accompany formation of an

amorphous surface are of tremendous interest because of the ease with which

amorphization can occur in specific systems.

Similarly, the mechanical properties of these phases as well as metastable

microstructures is of significant interest. Numerous examples exist on the

hardening of alloys by ion implantation and ion beam mixing. In many cases,

this translates into improved friction and wear properties of well-known engineering materials. The change in microstructure of the alloy surface has also

been found to strongly affect the fatigue and creep behavior of the component -

214 G.$. WAS

mechanical responses which are often associated with bulk properties of the

sample rather than surface properties. However, all of the observed property changes in metals are due to either

compositional, microstructural or topographical changes in the alloy. We must therefore, seek to understand how ion implantation induces these changes

before we can hope to understand their effects on the mechanical or physical

properties of alloys. Having accomplished this, we may then look forward to this

technique becoming a useful and reliable processing tool for the metals industry.

The purpose of this paper is to present an introduction and a review of the

state of ion beam surface modification of metals for property improvements. As

just discussed, property improvements can only be understood through a thorough knowledge of the compositional and microstructural changes induced

by ion bombardment of metals. Therefore, this topic is divided into two parts.

In this, the first part, compositional and microstructural effects of ion bombardment in metals are reviewed. The processes which govern the

composition profile of the implanted specie; sputtering, displacement mixing,

radiation enhanced diffusion, radiation induced segregation, Gibbsian adsorption

and preferent ia l sputtering, and the microstructural development ; phase stability, metastable phase formation, amorphization, dislocation dynamics,

precipitation, grain growth, etc. are discussed and reviewed. The second part will review the chemical; corrosion and oxidation, and

mechanical; hardness, wear, fatigue, property changes brought about by the

compositional and microstructural changes discussed here. The intent is not

merely to survey the current literature, but to present a coherent and

semiquantitative description and analysis of the physical processes occurring

during, or as a result of the ion bombardment process. Hence, a balance is struck

between the development of physical models and surveying the current

literature, resulting in a more pedagogical presentation.

2, Ion Beam Modification Techniques

The modification of metal surfaces by ion beams can be accomplished by a variety of methods, each with its own advantages for particular situations. The principal methods include 1) direct ion implantation, 2) ion beam mixing, 3) ion

beam assisted deposition and 4) plasma ion implantation and are shown schematically in Figs. 1-4. Each of these will be briefly described and considered

with respect to its advantages and disadvantages.

ION BEAM MODIFICATION OF METALS 215

@

©

6)

Fig. 1. Schematic representation of direct ion implantation.

Fig. 2. Schematic representation of the ion beam mixing process (IBM).

A w

A v

A w

~et

a f l u x

Plasma

sheath

Fig. 3. Schematic representation of ion beam assisted deposition (IBAD).

Fig. 4. Schematic representation of the plasma source ion implant ation process (PSII).

216 G.S. WAS

Direct ion implantation is accomplished by bombarding the target with a

beam of ions in the energy range from a few hundred keV to several MeV. The

beam is usually monoenergetic, contains a single charge state and is generally

(but not always) mass analyzed. Due to the stochastic nature of the elastic

collision process, the ions come to rest in a Gaussian distribution with the mean of the Gaussian centered about Rp, the projected range, with the FWHM ~

2.35ARp where ARp is the standard deviation from the mean.

Although seemingly a very simple process, this technique has several

disadvantages from the standpoint of modifying the surface composition. First,

the depth of the implanted distribution varies as E 1/2 and hence, energies in the

several hundred keV range, achievable in the most common implanters, will

only result in projected ranges of the order of 100nm for many ions. MeV

energies are needed to penetrate the micron range with heavy ions. Second,

sputtering will limit the concentration of the implanted specie to a value that is

the reciprocal of the sputtering yield. Since sputtering yields of metals at these

energies range from 2-5, the maximum concentration of implanted specie is 50%

to 20% respectively. The shape and location of the distribution can also be a

problem. In corrosion, where the composition of the top monolayer is most

important, the bulk of the modification occurs at considerably greater depths,

leaving the surface lean in the implanted specie. When the implantation induces

a phase transformation as well, the effectiveness or eff iciency of direct

implantation is lesser still. Finally, it is often desirable to implant metal ions into

pure metals or alloys to achieve particular surface compositions. As a practical

matter, most commercial implanters can produce large currents of inert gases,

but more elaborate measures are needed in order to produce metal ions at

currents which are practical. Ion beam mixing provides an alternative to the

shortcomings of direct ion implantation.

Ion beam mixing (IBM) refers to the homogenization of bilayers or

multi layers of elements deposited onto the surface of a target prior to

bombardment. The idea behind IBM is to create a surface alloy by homogenizing

alternate layers of the alloy constituents deposited in a thickness ratio so as to

result in the desired final composition following mixing. This greatly relieves

several of the shortcomings of direct implantation. First, the requirement of

producing a metal ion beam is eliminated since noble gases can be used for the

mixing. They are not expected to contribute a chemical effect in the solid and

yet can be made into high current beams in most commercial implanters.

Second, there is no restriction on the composition range since the final

composition is controlled by the ratio of layer thicknesses. This also removes

two other shortfalls of direct implantation; that of uniformity and surface


deficiency of the implanted specie. Ion beam mixing results in a very uniform

composition throughout the depth of the penetration. This includes the very

near surface region which is a problem with direct implantation. Finally, if the

elemental layers are made thin enough, the dose needed to achieve complete

mixing can be orders of magnitude lower than that needed to produce

concentrated alloys by direct implantation.

One further point is in regard to phase formation during or following ion

beam mixing. If the process is carded out at low temperature, the result is often

a metastable alloy in the form of either a supersaturated solid solution or an

amorphous structure. The microstructure can then be controlled by subsequent

annealing treatments. However, despite its many advantages, ion beam mixing

still suffers from the common disadvantage of limited depth of penetration. The

thickness of the surface is still governed by the projected range of the ion which

is in the 100 nm range for few hundred keV heavy ions. A solution to this

problem lies in the technique of ion beam assisted deposition.

Ion beam assisted/enhanced deposition (IBA/ED) refers to the growth of a

film with the assistance of an ion beam. In this technique, which is reviewed

extensively in Smidt [4], a film is grown onto a substrate by physical vapor

deposition using either an electron beam gun or an effusion cell, concurrently

with the bombardment by an ion beam. The advantages of this method are

numerous. First, there is virtually no limit to the thickness of film which can be

modified since modification occurs during growth. Second, ion bombardment

concurrent with vapor deposition provides for an atomically mixed interface,

resulting in greater adherence. The composition gradient in the interface can be

controlled by the deposition rate and the ion flux. Third, the enhanced mobility

of the surface during growth allows for the control of grain size and morphology,

texture, density, composition, and residual stress state. These properties are also

controlled principally by controlling the atom deposition rate in conjunction with

the ion flux (ion to atom arrival rate ratio), ion energy, fluence and species.

Hence, pure metals, solid solution alloys, intermetallic compounds and a host of

metal-base compounds can be grown by this technique.

A final technique which has recently been developed is plasma surface ion

implantation (PSII) [5]. In this technique, targets to be implanted are placed

directly in the plasma source and are then pulse biased to a high negative

potential (-40keV to -100 keV). A plasma sheath forms around the target and

ions are accelerated normal to the target surface, across the plasma sheath [5].

PSII has several potential advantages relative to conventional l ine-of-sight

implantation including 1) elimination of the need for target manipulation and

beam rastering, 2) elimination of target masking (retained dose problem), 3) the

218 G.S. WAS

ion source hardware and controls are near ground potential, and 4) PSII is

expected to be readily scaled to large and/or heavy targets.

However, all of these techniques involve energetic ion-solid interaction and

the physical processes that accompany this interaction. The following sections

address physica l p rocesses which affect compos i t iona l changes; recoil

implantation, cascade mixing, radiation enhanced diffusion, radiation-induced

segregation, Gibbsian adsorption and sputtering; and microstructural and phase

changes; phase stabili ty, metastable phase formation and amorphizat ion,

radiation induced grain growth, precipitation and dislocation dynamics. These

composit ional and microstructural changes form the basis for the observed

changes in physical and mechanical properties of the metal or alloy of interest.

3. Comoositional Chan~es

Immediately upon entering the solid, the ion begins to lose energy by

electronic excitation of the atomic electrons of the host atoms and by elastic

collisions with the shielded atomic nuclei. In metals, the electronic energy loss is

a major contributor to the slowing down of the ion, but it is the elastic collisions

which lead to atomic displacements. At high energy, the elastic collision cross-

section is low compared to the electronic energy transfer cross section and the

majority of slowing down is by electronic excitation. Those elastic collisions

which occur produce primary knock-on atoms in the keV energy range. As the

energy of the injected ion as well as that of the high energy knock-ons is

dissipated through both mechanisms, the elastic collision cross section becomes

very large and the mean free path between interactions is reduced to a few

Angstroms. The picture of energy transfer by elastic collisions changes from one

of sparse (few and widely separated), high energy knock-on production to the

production of a high density of low energy knock-ons. The result is a collision

cascade in which the kinetic temperature may reach 104-106°C and in which the

atoms interact in a collective fashion producing significant lattice disorder.

These dense cascades are characterized by either their temperature (thermal

spikes) or atom relocation (displacement spikes).

The temporal development of the cascade can be divided into three phases:

(1) a collisional phase which lasts between 0.1 and 1 ps, during which the energy

transferred to the primary knock-on atom is dissipated among successive recoils,

(2) a relaxat ional phase of about 0.5 ps during which Frenkel pairs

spontaneously recombine due to their close proximity, and (3) a cooling phase

lasting only a few ps in which the highly disordered cascade region cools to


reach equilibrium with the surroundings. The mixing which occurs in the first

two phases is termed ballistic, while the third phase involves collective behavior

giving rise to the term "thermal spike" to describe the distribution of of energy

among the atoms. According to the modified Kinchen-Pease model [6], the

number of displacements per target atom per second in a cascade is given by the re la t ion

P(x) = 0.8/(2NE d) (dE/dx) n 0, (3.1)

where ~ is the ion flux, N is the atomic density of the solid, E d is the effective

threshold displacement energy and (dE/dx) n is the ion energy deposited per unit

depth into atomic processes. Within a single cascade, the mean displacement

distance is always insignificantly small. For example, if each Frenkel pair is displaced an average of -10/~ (Rrecoil), because the ratio of the number of

displaced atoms N d, to the total number of atoms within the central core of the

cascade N v, is much less than unity, the mean atomic displacement due to

ballistic mixing within the cascade (Rrecoil x Nd/Nv) is negligible. Only with the

aid of radiation enhanced diffusion (due to the high defect concentration) after

the cascade has ended, could significant mixing occur. At doses > 1016 ions/cm 2,

the implanted region receives > 10 3 successive overlapping cascades and the

cumulative effect of ballistic mixing is no longer negligible.

The primary disordering mechanism is collisional or ballistic mixing which

can be qualitatively classified into recoil implantation and cascade (isotropic)

mixing. Recoil implantation refers to the direct displacement of a target atom by

a bombarding ion. Indirect processes involving other target atoms are

collectively called cascade mixing. Referring to experiments involving the

implantation into a bilayer or a thin marker layer embedded in a monatomic

solid, recoil implantation produces a shift and a broadening of a given initial

profile while cascade mixing produces primarily a broadening. But in addition to

collisional mixing, thermal processes may become important, leading to radiation

enhanced diffusion in the target and a greater degree of atomic mobility and

relocation than at low temperatures. In alloys at higher temperatures, when the

flux of defects to sinks becomes coupled to the counter flow of host atoms,

radiat ion-induced segregation can occur, resulting in the accumulat ion or

depletion of an alloy component at defect sinks. Finally, the sputtering of atoms

from the bombarded surface results in compositional changes in the near surface

region of an alloy and can only be explained using our understanding of the

processes just mentioned. The following subsections provide a development as

well as a review of the physical processes of recoil implantation, cascade mixing,

220 G.S. WAS

radiation-enhanced diffusion, radiation-induced segregation, Gibbsian adsorption

and sputtering.

A. Recoil imolantation

In alloys, the relocation cross section and the range of the recoiling atoms

depend on the charge and mass of the nucleus in such a way that generally the

lighter component atoms will be transported relative to the heavier components

in the beam direction. This can be described as a flux of atoms of some of the

alloy components toward deeper regions in the target, compensated by an

opposite flux of the remainder of components to maintain atomic density at the

proper value, i.e., the net flux of atoms is approximately zero across any plane

parallel to the surface inside the target. The expression "recoil implantation" is

used here for this net transport parallel to the beam direction of some types of

atoms relative to other types. The mechanics of recoil implantation have been

developed by Sigmund [7-91. He showed that an impurity atom knocked off its

lattice site by an incoming projectile ion has a relocation cross section that can be

estimated from LSS theory [10,11] as

dtsij(E,T ) = CijE-mT-l-mdT ,

0 < T < YijE, ij = 0,1,2,

and Yij = 4MiMj/(Mi + Mj)2,

(3.2)

where Cij is a constant, m is a parameter describing the collision (0<m<l) and is

usually taken to be a value of 1/2 for interactions in the keV range and 1/3 in the

eV range, E is the incoming ion energy and T is the energy transfer. The

impurity will, on average, be found at a depth

< z + x > = x + ~oJ" z d ~ s ( x , z ) , (3.3)

after bombardment by a differential fluence 80 , where

z = Rp(T) cos0, (3.4)

and Rp is the projected range and cos0 = (T/Y01E)I/2.

implantation <z> is

The mean recoil

<z> = (o~ + 1/2 - m)-lSOB(x)Zm(X), (3.5)


and the relocation profile of the impurity distribution is given by:

221

P(Ax) -Odo(x ,Ax) /d (Ax) , for large Ax. (3.6)

The quantity B(x) is of the order of nro2, with r o being the distance of closest

approach in an ion-impurity collision at depth x, and a is a constant between 0 and 2. As a rule of thumb, z m is less (greater) than the residual ion range R(x) at

x if the impurity is heavier (lighter) than the matrix. The total effect Pi, of this

knock-on implantation ( ~ number x range) is given by

R 70;E(x),.

Pi = Nci ~ dx J d(s0i [E(x),T] Ri [(T)/70iE(x)] 1/2 , 0 0

(3.7)

where N is the number density of atoms, ci is the concentration of alloy component i and E(x) is the ion energy at depth x., The range Ri(T ) is determined

by the partial stopping cross sections Sij(E ) = ~ Td(~ij(E,T ). After integration [7]

of eqn. (3.7) one finds

Qij = Pi/R = 70i2m-l(1-m)/m(l+2m) (ci/((Ail+Ai2)), (3.8) w h e r e

Aij = cj(Tij/70i) 1-m (aij/a0i)2(l-m) (Mi2/MoMj)m (Zj/Z0)2m. (3.9)

The quantity Qi is the equivalent number of i atoms recoil implanted over the

depth R (i.e. the ion range) in the direction of the ion beam per incident ion. The dominating term in Qi with regard to its dependence on the target composition is

M i2rn. The dependence is such that recoil implantation of the lighter species

dominates that of the heavier one. Although the number of i recoils at a given energy (T,dT) is dominated by the heavy compone~nt (as Mi -m Zi2m), the range of

i recoils at a given T is a Mi -m Zi -2m and so the combined effect is greatest for

the lighter species. Equation (3.5) also indicates that the mean relocation due to

recoil implantation should have a linear dependence on fluence.

Sigmund applied this formalism to the case of argon bombarded PtSi [7] and determined that Qpt = 0.034 and Qsi = 0.37 for m = 1/2, and QPt = 0.19 and Qsi =

0.94 for m = 1/3. Both cases predict a net transport of Si that is considerably

greater than that for Pt, Fig. 5. Results of Liau et al. [12] provided initial support

for this model. Paine [13] conducted experiments on a sample of the same

222 G.S. WAS

geometry as described by Sigmund [7] using 300 keV Xe + at 90K to fluences up to 1.27 x 1016 i/cm 2, Fig. 6.

103 I r r I ; I l I J I / ' i f I I I 1 I | sputtered layer thickness,--",, sion-motrix I~nockofl ~1

, .~" , / Cme°n sh,ft) -I v~ /'~/'-~,L'-~tota[ matrix knockon /

exp ~_ ,,~ / " (mean shift) - - /

(HWHH) / ~ / /ion-in~ourity knockon | 300 keY Xe 1 ~ / / , / (mean shift) 4

- on Pt in $i / o,,,o, / / / I 10 2 Ira=0.5; c<=1}

/ ion-impurity knoekon

i / / / 1

S " / / t , ' " / , / , iZI I I I i l l I J ', I I /

lOlo~s 101 1017 Pluence lions/emil

Fig. 5. Marker layer shift for 300 keV Xe ions incident on a thin Pt layer at 750/~ in Si calculated using Sigmund's recoil implantation model. (from ref. 8)

12

t ~8

o 6[

g2 m<o

I I l I I

IRRADIATION ~ Pi SIGNAL 300 key Xe + SAMPLE t j NO. I 8 2 × 1015 Ions/cm 2 70.50 ~,I

l,, 1.5 MeV He* P! SIGNAL 1 NO. 2

A ,\ SAMPLES : ~UNIRRADIATED IMPURITY~

I ~ I R R A D I A T E D IMPURITY ~ - ~ / ,~ / I R R A D I A T E D IMPURITY" I / 'i p MINUS IRRADIATED BLANK \ g~ /

09 1.0 I. I 1.2 1.3 ENERGY (MeV)

Fig. 6. Backscattering spectra recorded with the unirradiated impurity sample (continuous lines) and the impurity sample irradiated to a fluence of 8.2 x 1015 Xe ions/cm2 (open circles). (from ref. 13)


He found a negative shift, that is, a net transport of Pt away from the surface, in

direct contradict ion with Sigmund's matrix relocation theory. The linear

dependence on fluence was verified in these experiments, Fig. 7. M a n t l e t al.

[14] conducted mixing experiments using dual markers consisting of thin

adjacent layers of Au and Ni or Pt and Ni in either Si or A1. Mixing with 300 keV

Ar + at 20, 80 and 300K to doses up to 1 x 1017 i /cm 2 caused a small (2-5 nm)

negative shift of Ni to the surface, relative to Au or Pt. These results support the

observations of Paine for net transport of the lighter specie toward the surface.

More recently, Auner et al. [15] conducted mixing experiments on Hf-Zr bilayers

and found that the dominant moving specie is the result of a anisotropic atomic

transport which is determined primarily by sample geometry.

I00 , ,

I SK~MUND AND _ ~ - - ~ / GRAS - MARTI----,~..q~ ~

5 0 ~ ~ ~ ~

0 ~

-200 / i I 0 5 I0 15

FLUENCE (IO 15 ions/~m 2)

Fig. 7. Shift in the mean position of the Pt layer (diamonds) caused by 300 keV Xe irradiation, plotted against irradiation fluence. Posit ive shift indicates movement toward the sample surface. The dashed line is the calculation by Sigmund and Gras-Marti [8] for a dilute Pt impurity buried at a depth of 750 ,/~. (from ref. 13)

Rousch et al. [16] conducted Monte Carlo simulations on ion bombarded alloys

consisting of 2 components with equal binding energies. They found that there

is a preferential movement of the heavier species inward, due primarily to the

recoil cascade. Recently, Littmark [17] has conducted theoretical calculations on

marker shifts based on transport theory and including a lattice relaxation effect.

Calculations for 300 keV Xe + bombardment of Pt markers buried in Si and 400

224 G.S. WAS

keV Xe + bombardment of W markers buried in Cu at different depths predicted marker shift direct ions which are in agreement with observa t ions in

exper imen t s .

B. Cascade (isotrooic. displacemenO mixing

A collision cascade generates a large number of recoils in the low energy

range with displacement distances on the order of a few atomic distances.

However, because the collision cross section increases with decreasing energy,

the number of such events can become extremely large compared to relocation

b y recoil implantation and so matrix relocation by low energy events can

dominate the picture. Although the ion fluence generates an anisotropic

distribution of knock-ons, the statistical independence of subsequent events

produces nearly isotropic mixing which can be characterized by a random walk

of the impurity. As long as the total relocation Ax is small enough so that the

relocation cross section does not vary significantly over this distance, the mean relocation can be described by [8]:

<Ax> = Oj'z do(x,z), (3.10)

and the mean spread by

~2 = <(Ax_<Ax>)2> = • J" z 2 do(x,z). (3.11)

The relocation profile becomes

P(Ax) = 1/2~ f exp(ikAx-Oo(k)) dk, (3.12)

w h e r e

o(k) = f (1-e -ikz) do(x,z) . (3.13)

For elastic collisions, the relocation cross section is given by

do = dz F(FD(x)/N) f (dT/T2)(S21(T)/S22(T)) f (d2tT/4~)Fl(T,fl ' ,z), (3.14)


where $21 and S22 are stopping cross sections for matrix-impurity and matrix-

matrix col l is ions, respect ively , F is a dimensionless parameter, F o is the

deposited energy per unit depth and F1 is the range distribution of an impurity

with initial energy T and recoil direction f t . This expression can be simplified using a well-defined impurity range relation [10,11], Rp(T) = AT a yie lding

do(x,z) = F(FD(x)/N)~21 [2(a+l) ] -1 d(z/A) (Izl/A) -1-11a, (3.15)

where g12 = S12/S22. For recoils in the eV range, the relocation profile becomes Gaussian with <Ax> =

0,

P ( A x ) - (2gf~2) -1/2 exp[-(Ax-<Ax>)2/2g22], (3.16)

and the spread is given by

f~2 = 1/3 (1-2a) -1 ( F / N ) • F D ~21 (Rc2/Ec) = 4D't , (3.17)

yielding an effective diffusion coefficient,

D* = 1/12 (1-2a) -1 ( F / N ) ~ F D ~21 (Rc2/Ec). (3.18)

where E c is a minimum threshold recoil energy corresponding to a minimum

displacement distance, R c = AEca. A similar expression was also developed by

Andersen [18] by assuming that since cascade mixing is isotropic, then the result

is a cumula t ive random-walk- l ike d i sp lacement process which can be

characterized by an effect ive diffusion coeff ic ient D*, analagous to that

developed in the atomistic model for thermal diffusion,

D* = 1/6Z,2P, (3.19)

whe re 2~ is the root-mean-square separation for a vacancy-interstitial pair and P is given by eqn. (2.0). The resulting equation for D* is

D* = (1/6) (0.8/2NEd) (dE/dx)n X 2 ~, (3.20)

which is essentially the same expression developed by Sigmund [8], eqn (3.18).

The effect of cascade mixing is to smear out an originally sharp interface or to

broaden a delta function to a Gaussian distribution. For an infinitely thin layer

226 G.S. WAS

of element B in element A, the solution of Fick 's second law gives the

concentration as a function of position at any time as

C(x,t) = it/2 (~D*t)-l/2 exp (-x2/4D*t), (3.21)

where o~ is the amount of initial amount of element B. The concentration profile

for a pair of initially semi-infinite solids is

C(x,t) = a/2 [1 + erf (x/2 "(D-'~)], (3.22)

and for a thin film of thickness a,

C(x,t) = ix/2 [erf (x/2"~-D-t) - erf (x-a/2,/-D*t)]. (3.23)

From eqn. (3.17), which relates D* to D 2, the concentration profile can be

determined directly. Note that broadening is proportional to ((~t) 1/2. In terms of

experimentally measured spectra,

~2 to t a I = f22unirra d + D2mixing , (324)

D2tota I = D2uni r ra d + 4D*t. (3.25)

Sigmund [8] calculated the broadening of an initially narrow Pt layer in Si as a

function of ion fluence for both low energy and high energy cascades, Fig 8. He

found that up to ~ N 1 0 16 ions/cm 2, the ion-impurity knock-on profile is

determined by single events, while at ~ = 1 0 1 7 i o n s / c m 2, a multiple relocation

profile emerged. At the highest fluence, 1017 ions/cm 2, high- and low-energy

isotropic cascade mixing yield comparable contributions both within and beyond

the halfwidth of the distribution.

Many experiments have been conducted to measure the mixing under ion

irradiation. They center about either mixing of bilayers or multilayers, or

broadening of thin marker layers. Matteson and Nicolet [19] gave a nice review of ion beam mixing experiments using these three geometries. Paine measured

the broadening of a Pt marker layer buried in Si in the same experiment used to

determine the marker shift [13]. Both Sigmund and Gras-Mart i [8,20] and

Matteson et al. [21,22] predict a linear dependence of f~2 on ~), as is observed in


Paine's [13] results, Fig. 9. However, the gradient of the curve is inconsistent

with that measured by experiment by about a factor of 2. Matteson et al. [22]

conducted mixing experiments on marker layers of Ni, Ge, Pd, Sn, Sb, Pt and Au

in Si using Ne, Ar, Kr and Xe ions at 50, 110, 220 and 300 keV, respectively. The

energies were selected to yield equivalent projected ranges and the doses were

selected to give approximately equal amounts of mixing using estimates based

on the premise that the mixing is approximately proportional to the product of

the dose and the nuclear stopping power. Results confirmed that the mixing

parameter Dt is proportional to (~ over a wide range of doses. The data is also consistent with Dt/d)being proportional to (dE/dx)n/Rp, the ratio of the total

nuclear energy loss of the mixing ion and its projected range.

103 . . ~ [ I I I [ r I l I I / ' ~ "~ [ 1 I I [ w _ total matrix knockon ~J"~$puttered layer thickness .~ _ ( rm S ) \ f ~ / /

' x P ' / ~ / / / / (HWHM) ~P ,/ J / impurity kne£kon 300 keY Xe ~ - . ~.~

on Pt in Si / exp..a~./" i ' ' " (r.m.$.)

,0, / / / / / h i ~ energy cos, code

-- / / / / / s / mixing (HWHM) - - / s p S

/" / / / ~ i m p u r i t y kno£kon (HW HP 10 / " ~ t I I i I / I t ! I I l I I l

10 )5 1016 1017 Fluence (ionslcm z)

Fig. 8. Broadening of the marker layer for 300 keV Xe ions incident on a thin Pt layer at 750 /~ in Si (same geometry as in Fig. 7) calculated using Sigmund's relocation model. (from ref. 8)

However, Wang et al. [23,24] have studied the mixing behavior for collisionally

similar systems, Cu-Au-Cu and Cu-W-Cu using the same structure for the

samples for both systems. It was found that in the case of the Cu-Au system,

peak broadening is an order of magnitude larger than that in the Cu-W system.

Other collisionally similar systems, AI-Sb-A1 and AI-Ag-AI studied by Picraux et

al. [25] showed the mixing rate in the AI-Ag system to be 2.6 times that in the

AI-Sb system. Other discrepancies in mixing rates have been found and a

complete review of mixing experiments has been conducted by Paine and

Averback [26]. They found that mixing depends on several parameters. First,

228 G.S. WAS

A.0 . - " + T

] ! ' , , - " ] T

• ,

o 5 io FLUENCE (1015 ions/cm 2)

Fig. 9. Variance t~ 2 of the irradiation-induced mixing of the Pt layer plotted against irradiation f luence (fi l led circles). The open circles are the measurements by Matteson et al. [21], scaled by the appropriate ratio of values of F D for a layer depth of 500,~. The dashed line is the calculation by Sigmund and Gras-Marti [8]. (from ref. 13)

the profiles in marker layer systems after mixing are almost always Gaussian as

expected from theory. For both markers and bilayers, mixing appears to be

independent of temperature below ~80K. The parameter, Dt, does not vary with the irradiation flux ¢, but it is linear with fluence, ~ , below T c, the characteristic

temperature below which thermal processes become negligible. Below T c, Dt generally varies linearly with F D. However, Xe ions produce a factor of 2 more

mixing than N, Ne Ar and Sb ions in Ni(Au) marker layer systems. Also, for Si/Pt

bilayers at low temperatures, mixing efficiencies for heavy ions (Kr and Xe)

were greater than for light ions (He and Ne) by about a factor of four.

Fu-Zhai and Heng-De [27] used a Monte Carlo code to simulate the

transportation process of an incident ion and the cascade of all recoils in an

elementary amorphous, bilayered target. They found that the interface mixing

was remarkably sensitive to the interface potential (between layers A and B).

Further, primary recoil mixing contributes only 9.3% of the total mixed Sb atoms

in a Sb/Si bilayer target, while long range mixing contributes nearly 50%.

However, most of the mixed atoms come from a distance within 20-30/~ from the interface.

Paine and Averback [26] have also reviewed the mixing of marker layer efficiency in Si and Ge, Fig. 10 and A1203, SiO 2 and metals, Fig. 11 as a function of

the z of the marker. As shown, the collisional model of Sigmund and Gras-Marti


[8] cannot explain the large variation of the results with marker species. Such

large differences in mixing efficiency between different markers suggest that

the chemical nature of the marker must play a role.

1 5 0 ' ' ' ' ' ' ' = ' G . ' 1 5 0 Ion boom =~x=n 9 oF ~ k ~ . ~

tt~ r < I00 I( ~ Au

\I 7\, +,, ....

0 J - - t - - ' ~ - - [ ' - 7 - - T - - f - - 7 " " L

0 1 0 2 0 : 3 0 4 D 5 0 (50 7 0 8 0 9 0 1 0 0 Z ( Id~-k~)

ioo

= 50

Fig. 10. The efficiency of marker mixing Dt/~>FD, plotted as a function of the atomic number of the markers in Si and Ge media. The plotted points are the averages of all reported data for irradiations below 100K. The dashed line is calculated from the low energy collision cascade model of Sigmund and Gras-Marti [8]. (from ref. 26)

^ 1oo %

~ 50

=n ,Nta l ~ d ox=de ~md=o T ~ • '00 K

i g*d:~ 0 AI

A AI203

V S~02

D Fe

• NI

• Eu

• HF

. . . . . . . ~ ' ~ Jr" 0 I I I - - I - - -- T - - - - f - -- 7 - - -- "F I

0 10 2 0 3 0 4 0 5 0 6 0 7 0 8 0 gO l O 0 Z (Morkur)

Fig. 11. The efficiency of marker mixing, Dt /¢FD, plotted against the atomic number of the marker for metal and oxide media. Again, the plotted points are the average of all reported data for irradiations below 100K. The dashed line is calculated from the low energy collision cascade model of Sigmund and Gras-Marti [8]. (from ref. 26)

C. Chemical effects

Bilayer mixing rates have been found to depend strongly on the nature of the

layers as noted earlier in experiments on Cu-Au layers where the mixing was an

order of magnitude greater than in Cu-W layers [23,24], and in the greater

mixing rate (by a factor of 2.6) in Ag/A1 as compared to Sb/Ag [25]. d'Heurle et

al. [28] found that the chemical affinity of the elements has a controlling effect

on the amount of mixing which is obtained. Minimal mixing is observed with

pairs such as Zr/Hf or Pd/Pt, and maximal mixing with pairs such as Zr/Pt or

Pd/Hf. The results imply that a high chemical affinity between the elements

results in high mixing. Cheng et al. [29] also noted a strong chemical effect and

was able to show that the mixing rates could be correlated in a linear manner

with the liquid alloy heat of mixing of a given metal pair, Figs. 12 and 13. In

1985, Johnson et al. [30-33] proposed a phenomenological equation to account

for the observed chemical effects, based on the presumption that the dominant

230 G.S. WAS

contribution to ion mixing occurs when particle kinetic energies are of order

leV, and properly accounting for the Kirkendall effect to describe diffusional

intermixing in non-ideal solutions.

8.0

6 0

4 0

2 0

• ~ o( "o

6.C

4.C

2.C

O.C

6OO keV XC*, 7 7 K ~. PITI

- ~ P t M n

AuCr

0 l 0 I.O 3.0 5 0

DOSE (I Ol%t/cm z )

25

2 0

~u~ L.J o

6 0 0 keV Xe'*, 7 7 K

AuTi

2 - P,,,__~'-+=-" ~ff~,v

2'5 5b ,'5 ,;o ,~5 -AHm(kJ /g - of)

Fig. 12. Variance of interface profile vs dose for se lec ted b i layers irradiated with 600 keV Xe ++ at 77K. (from ref. 29)

Fig. 13. Correlation between mixing parameter and Miedema 's heat of mixing for various bilayers irradiated with 600 keV Xe ++ at 77K. (from ref. 29)

Johnson argues that although recoil mixing in the ballistic regime yields a

density of displaced atoms at a given distance from the interface which is linear

with ion fluence, low energy mixing in a well developed cascade can be

described by a random walk or diffusional process [18,34] which will dominate

ballistic mixing in well developed cascades [29]. In fact, the measured mixing

rates for different pairs of elements can be accounted for by replacing the

diffusion coefficient in Fick's law by a modified D' which accounts for the

Kirkendall effect and describes diffusional intermixing,

D ' = Do' [1 - 2AHmix/kT], (3.26)

where AHmi x = 26CACB,

and 8 = [VAB - (VAA + VBB)/2],

where VAA , VBB and VAB are the potential energies of the interaction of the

respective pairs. Physically, this equation says that a random walk will be


biased when the potential energy depends on the configuration. This equation can be fit to the data [29] to obtain a value of kTcff = 1-2 eV, indicating that

chemical biasing can only contribute to ion mixing when the particle kinetic

energies are of order 1 eV. Since strong chemical effects have been noted, this

implies that the dominant contribution to ion mixing occurs in the 1 eV range!

Johnson [30] postulates that the effective diffusion constant per unit dose rate

can be described by an equation of the form

4D't/tb = Kle2/(p5/3 AHcoh 2) [1 + K 2 (AHmix/AHcoh)], (3.27)

which can be used to predict mixing profiles for an arbitrary metal bilayer with

well developed cascades in the thermalizing regime, Fig. 14. In this equation,

is the energy deposited per unit path length, p is the average atomic density of tile target, AHco h is the binding enthalpy per atom and K 1 and K 2 are constants.

The condition for well developed cascades can be stated in terms of a critical value of e/AHco h >> tz C, where ¢C is the critical value for which ballistic recoil

mixing is comparable to diffusive mixing.

Recently, de la Rubia et al. [35] have conducted molecular dynamics (MD)

calculations of 3 and 5 keV cascades in Cu to show that, indeed, the central

region of the displacement cascade shows considerable disorder, Fig. 15, and the

radial pair-distribution functions, g(r), for the cascade region are quite similar to

that of liquid Cu, Fig. 16. The prompt region of the cascade evolution is divided

into two subregimes; the ballistic regime or collisional phase in which atomic

displacements up to 0.1 ps are well described by ballistic mixing theory, and the

thermalizing regime or cooling phase (t=10 ps) during which atomic mixing

occurs by a diffusional process. Using these definitions for the respective

temporal zones of the cascade, the authors concluded that the majority of the

mixing occurs in the region of the melt and is not associated with Frenkel-pair

production. They observed that only a relatively small fraction of the atomic

mixing takes place up to 0.12ps (roughly the end of the collisional phase),

whereas the vast majority of the mixing occurs during the thermal spike (t =

10ps) and can be accounted for by diffusion in the locally melted region, Fig. 17.

Further, energy densities are typically of the order of 1-10 eV/atom and the

mean time interval (<l .0ps) between collisions in this energy range is small

relative to the lifetime of the cascade. These results are consistent with

observations of a chemical effect of mixing (which could only occur if mixing was

dominant in the eV/atom range) and support Johnson's phenomenological model.

The results are supported by those of Webb et al. [36] who showed melting in 5

keV Ar + bombarded Cu within 0.2 ps. Most recently, Ibe [37] has shown that

232 G.S. WAS

the amount of mixing is equally dependent on the heat of mixing for alloy formation and the intrinsic diffusion coefficients. Hence the present picture of mixing in ion irradiated solids can be summarized by the following:

0 3 0

. ~ 0 25

:~L o~o < ] : w

Q~ 0 1 5

~ - o~o

005

0 . 0 ' t:'1 t~u 1

O 0 0 0 5

;p f ~r /

• / H f Pd

9~f Bib

0 Hf Ru

~ H f A £

I l I 0.10 0.15 0 . 2 0 0 , 2 5

A H m ~ / A H c o h

Fig. 14. Correlation between the normalized mixing parameter and AHmix/AHcoh for bilayers irradiated with 600 keV Xe + + , and for K1=0.034/~ and K2=27. (from ref. 31)

2.8 ~ 5 keY PKA in Cu 4 zx o ',,~_ t = l l ps 2 4 ~

" ; ; ~ t=5.8 ps ~ L ° ~ --- calculated for

~'.u ¢ ~ ',quid Cu

o.8 r o.0 ! - - t

O b - - a ~ I , I ~ I , I , I q .5 2 .5 3.5 4 .5 5.5 6.5

Rodius(~)

Fig. 16. Radial pair distribution functions, g(r), corresponding to the disordered zones at t= l .10 and 3.84 ps. Distribution function for liquid Cu is included for comparison. (ref. 35)

120

I00

8C

60

4O

2O

÷ . ~ % ~ g % . % % % ÷ 4 * ÷ * ÷ ÷~.÷ + ÷ ÷ ÷ ÷ ÷ • ÷ ÷ 744" ÷ ÷ ÷ * $%%%T~ ÷*.÷%÷÷.*÷~;**~ ÷ % % ÷ ÷ ; ÷ ; ÷ ; ÷ , + ; ÷ ÷ ÷ %+÷÷~.+ * ÷ ÷ ÷ ÷

÷÷Z.+Zt;t÷t.÷÷*÷.÷*÷*÷t:.+;tZ*÷÷.÷.g÷;÷~÷:~;t+++÷

~ . t ÷ ÷ ÷ * ÷ ÷ * * ÷?÷%%%%%÷;~" ÷% ÷t i t ;%%.* ; *~ ÷ ~ ÷ ~ . ÷ ÷~÷: ;.%%t;*.÷ ÷ ÷t+*

. ~ . * ~ : ; % t ; , . + ; * i ÷ i ÷ ~ , i ~ i * ~ : ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ * ;÷ % t ÷ : ÷ ÷ ÷ r ÷ : - ÷ ~ ÷ : ÷ : ÷ : ÷ : * +*%~;÷~'~'I '%'~'I '%'t;% ~..+,÷* ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ + ÷ + ÷ ÷ ÷ + ÷ ÷ ÷ ÷ ÷ + ÷ ÷ ÷ ÷÷ + ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ *

÷ ÷ ÷ * ; ,%$~ ,÷ ÷ ÷ ÷ % ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ % ÷ ~ , * ÷ ÷ ÷ ÷ ÷

• ÷.~'bi- ÷ + ÷ ÷ * ÷ ÷ ÷ ÷ :i-~.i-+4- ÷ ÷ ÷ ÷ ÷ ÷~.÷,~÷ ÷ ÷ ÷ ÷ ÷ ÷ + ÷ ÷ + ÷ ÷ ÷ ÷ ÷ + + ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ + ÷ ÷ + ÷ . + ; ÷ ~ . ÷ ; ÷ ; ÷ ; * +

I I I I I I

2O 4O 60 80 I00 12O Y(~,)

Fig. 15. Locations of atoms in a (100) cross sectional slab of thickness ao/2 through the center of a 5-keV cascade at t=l.1 ps. (from ref. 35)

50 ' I i I

5 KeY Cascade

Cu

..o % ic

o IO 20 50 40 Rodius(~)

Fig. 17. The integrated diffusion coefficient as a function of distance from the center of the cascade at the end of the collisional phase, t=0.12ps (diamonds) and at the end of the cool ing phase, t=10.0ps (squares). (from ref. 35)


1) The core of the cascade region resembles that of a liquid,

2) mixing in the 1-10eV/atom range strongly dominates that at higher

energies, and

3) because of 1) and 2), chemical effects can strongly affect the extent of

mixing in all systems.

Although this description describes the situation at low temperature, as

temperatures increase, radiation enhance diffusion begins to play a role in the

observed mixing.

D. Radiati0n-enhanc¢O diffusion

In the absence of radiation, the diffusion of vacancies and interstitials is

characterized by a random walk process which is described by an equation of the form

D = Doexp(-AHm/kT ), (3.28)

D O = Ctao2V exp((ASth + ASm)/k), (3.29)

where (t depends on crystal structure, a o is the lattice parameter, v is the Debye

frequency, ASth,m are the configurational and mixing entropies, respectively,

AHrn is the defect migration enthalpy, k is Boltzmann's constant and T is the

temperature. In the presence of irradiation, the thermally-act ivated free

migration of irradiation-induced vacancy and interstitial defects is known as

radiation-enhanced diffusion (RED). Sizmann [38] has written a comprehensive

review of RED including dependencies on temperature, dose and dose rate. He

notes that diffusion can be significantly enhanced under irradiation by either of

two mechanisms: (1) by increasing the concentration of defect species, e.g.

vacancies and interstitials which normally provide the means for atom mobility,

and (2) by creating other diffusion mechanisms via defect species which are

usually not operative. Since the diffusion coefficient is a linear superposition of the various diffusion paths, then

Dir r = fvDvCv + f2vD2vC2v + fiDiCi + .... (3.3o)

where the fs are correlation factors, usually < 1. Thus the determination of the

diffusion coefficient depends on the concentrations of vacancies and interstitials.

234 G.S. WAS

The local change in defect concentra t ion of the var ious defect species can be

wr i t ten as the net resu l t o f the local p roduc t ion ra te , r eac t ion ra tes and

d ivergence of flow. The result ing rate equations are

dCv/dt = K o - KivCiC v + KvsCvC s + VDvVCv,

dCi/dt = K o - KivCiC v + KisCiC s + VDiVC i,

(3.31)

(3.32)

where K o is the point defect product ion rate and Kiv, Kvs and Kis are the rate

constants for the react ions indicated by the suffix combinat ion . Note that these

equa t ions accoun t for loca l ized sinks by inc lus ion of the last t e rm in each

express ion as well as un i fo rmly dis t r ibuted sinks. Thei r solut ion requires the

s ta tement of boundary condi t ions in addit ion to the initial local concent ra t ions

Ci,v(r) of the mobi le defects i,v. However , if the mean defect separation is larger

than the m e a n d i s t ance b e t w e e n e x t e n d e d de fec t s , or the s inks can be

homogen ized without loss of accuracy, then the chemical rate equat ions become

dCv/d t = K o - K ivCiC v + KvsCvCs, (3.33)

dCi]dt = K o - KivCiC v + KisCiC s,

Dir r = DvC v + DiC i .

(3.34)

(3.35)

The s teady s tate concen t ra t ions are de t e rmined by so lv ing eqns (3.33) and (3.34) with both dCv/dt and dCi/dt taken equal to zero, giving,

Cv(S) = -KisCs/2Kiv + [KoKis/KivKvs + Kis2Cs2/4Kiv2],

Ci(S) = -KisCs/2Kiv + [KoKvs/KivKis + Kvs2Cs2/4Kiv2].

(3.36)

(3.37)

Note that the s teady state concentra t ions of vacancies and interst i t ials g ives the

dependenc ies on the tempera ture , sink concent ra t ion , total dose and dose rate.

In par t icular , at low t empera tu re and for low to in te rmedia te sink densi t ies ,

r e c o m b i n a t i o n d o m i n a t e s loss to s inks and the v a c a n c y and in te r s t i t i a l

concent ra t ions can be approx ima ted by

C v = (KoKis /KivKvs) l /2 ,

C i = (KoKvs /KivKis ) l /2 ,

(3.38)

(3.39)

g iv ing


Dirr = (~KoDv/47rRivN)l/2 + (13KoDi/4~RivN)l/2,

235

(3.40)

where I~ is the fraction of v-i pairs still present in the delayed regime. This

quantity is proportional to the product of dose rate and diffusivity to the 1/2

power. At high temperatures, the steady state concentrations of vacancies and

interstitials is given by,

C v = Ko/KvsCs, (3.41)

C i = Ko/KisC s. (3.42) Given that

C s - n2/L2(f~/4nRvs,is), (3.43)

then the diffusion coefficient is

Dir r = 2~KoL2/n2, (3.44)

which is directly proportional to the dose rate and the square of the mean

distance L between extended sinks. Figure 18 shows the steady state defect

concentrations for an irradiated solid at high and low temperatures for high and

low dislocation densities [39]. Figure 19 shows the resulting radiation-enhanced

diffusion coefficient in a Ni foil due to ion bombardment at typical dose rates.

In traversing from low to high temperature, ion beam mixing shows an

increasingly pronounced dependence on the sample temperature. Matteson [34]

found that below 300K, broadening of Ni, Ge, Pt and Au in Si by 200 keV Kr+ or

300 keV Xe + was temperature independent up to 300K and up to 523K for Sn

and Sb. However, he also showed [40] that in Nb-Si, mixing became strongly

temperature dependent above -600K, Fig. 20. The temperature at which mixing

becomes strongly dependent on temperature is called the critical temperature, To. It is also defined as the narrow temperature range which separates the

temperature-independent region from the Arrhenius-type radiat ion-enhanced

diffusion region, or by the intersection of the high- and low-temperature asymptotes. Various authors have used the occurrence of T c to deduce the

specie responsible for the observed mixing behavior. Cheng et al. [42] describes

the behavior of the amount of mixing by an effective diffusion coefficient of the fo rm

D = D c + Dir r exp(-Q/kT), (3.45)

236 G.S. WAS

10-3

10 4

i l 0

u.

10 -6 >

10 /

OG

' ' / I \ / / , / / E,~u,,,o ..... / / / / ~ ' -

/ / / , , ' - \ / / / , , ' -

/ / . , , -- ~ / ii/ iiii - -

_ / iiii///// _

I 1

I 1 1 0 1 5 2 0

10L T. K 1

Io-~ I I

~0_~ ~ I iii /

l o ~3 ~]/// • Eqwhb~lucq

OL~ 1 0 1 5

1 0 J , T K (a) (b) t 20

Fig. 18. Steady-state point-defect concentrations in an irradiated solid at a high defect production rate (solid line) and at a low defect production rate (dashed line). The upper and lower curves for each defect production rate represent small and large dislocation densities, respectively. (from ref. 39)

TEMPERATURE (*C)

10_12 900 600 400 200 I00 0

,o-,, - , ~ ~ ,.,oo. I]

~J - - %~ ~ . . . . . . . . ION-BEAM" ""

~ o ; ,,,o,~ ~ _

l iT (10-3 K -I )

Fig. 19. The mean radiation-enhanced diffusion coefficient in a 500/~ thick foil of Ni at a damage rate typical of ion bombardment, calculated from the analytical solution to the rate equations. A sink density of 1010/cm2 was assumed. The curve shown represents a somewhat idealized picture, in that saturation of the vacancy concentration and time-dependence of the defect concentrations at low temperature have been neglected. The thermal diffusion coefficient and the diffusion coefficient due to ballistic mixing are also shown for comparison. (from ref. 41)


400 3 0 0 2 0 0 IOO

g,

-rl ',/ , , ^, Ii , .oucEo

I I IEA=0.9eV 211E,:2.'ev ~ t

25 "C r

- 2 .5

2.O

1.5

u

o

-;.0 ~ o

I 2 3 I000 (.K_l)

T

0.5

Fig. 20. Logarithm of the quantity of intermixed silicon versus reciprocal temperature for a fluence of 1.2 x 1017 28Si+/cm 2. The solid line is a fit to the data points of the sum of a temperature independent part (dotted line A) and a thermally activated part (dotted line B) with an activation energy EA- 0.9 eV. The quantity of intermixed silicon which would be produced by thermal silicide growth without irradiation in the same time interval is included in the figure for comparison. The scale on the right is for coefficient 13 where Q = ~1 /2 . (from ref. 40)

where the first term on the right-hand side is due to cascade mixing and is

temperature independent, and the second term is due to radiation-enhanced

diffusion and has an Arrhenius-type temperature dependence, where Q is an apparent activation energy. At a temperature near T c, the two terms on the

right of eq. (3.45) contribute equally and

T c = (1/k)[ln(Dirr/Dc)]-lQ. (3.46)

238 G.S. WAS

Assuming the existence of a scaling relationship between Q and the cohesive

energy of the matrix, Ecoh, i.e., Q = SEco h, then eqn (3.46) can be written as

T c = (S/k)[ln(Dirr/Dc)]-lEco h. (3.47)

A correlation between T c and Eco h is given in Fig. 21 for 10 binary systems,

verifying the predicted linear relationship. Cheng estimated that the average value of ln(Dirr/Dc) N 11.6, and from the slope of the line determined that S-0.1

and Q-0 .1Eco h. Since EmV = 0.24 Eco h by the same scaling relationship,

Q~0.12Eco h. Cheng concludes that this value for the activation energy (half of

the vacancy migration energy) is consistent with a model based on a vacancy

mechanism for radiation enhanced diffusion [43,44]. This result is also

consistent with the work of Sizmann [38] which shows that at steady state, the activation enthalpy for Dir r is 0.5Hm v. This yields a value of 1.03eV for the

vacancy activation enthalpy in nickel which is consistent with the assumption

that in Stage III vacancies are mobile.

I(30(]

80C

-~ 60C

40C

20C

• METAL o SILICIDE

p

ToSi

P~ Pd~ Au NI,/,~C~S NiPt

AFS

Eco h AVERAGE COHESIVE ENERGY (eV/atom)

Fig. 21. Correlation between the cohesive energy of the system and the critical temperature Tc at which radiation-enhanced diffusion becomes dominant. (from ref. 42)

However, Rauschenbach has observed that T c is often well below stage III and

along with Peak and Averback [45] has concluded that because of its high

migration enthalpy "normal" vacancy migration does not contribute significantly


to mixing. Rauschenbach [46] has proposed that the observed T e is in fact, due

to the migration of mixed dumb-bells via orthogonal jumps into nearest-

neighbor posit ions. From this he has developed an expression for the characterist ic temperature T c by equating the diffusivity due to vacancies and

interstitials at T<T c to that due to diffusivity by mixed dumb-bell migration at

T>Tc:

T c = (l /k)-HmV/[ln (Ko/Cs21~) - In (2Vv/Vcacv)], (3.48)

where Vv,c is the Debye frequency for vacancies and complexes, respectively, and acv is the recombination coefficient. The calculated values of T c were

compared to measured temperatures, Tcexp for 5 marker layer systems and 8

bilayer systems with considerable success.

The observation of low onset temperatures for enhanced mass transport in

ion-beam mixed systems has been noted by Rehn and Okamoto [47]. The

authors have suggest that enhancement in mixing at temperatures too low to be

due to the free migration of irradiation-induced vacancy and interstitial defects

may be due to intra- or inter-cascade mechanisms. This can be confirmed by

observing the dose rate dependence of D.

E. Radiation-induced segregation

The first experimental observation of radiation-induced segregation was made

in 1974 by Okamoto and Wiedersich [48]. Since that time, a complete theory for

the mechanism of RIS has been developed [49-58] and cons iderable

experimental evidence exists [59-70] to support the theory. RIS can be classified

as non-equilibrium segregation which is driven by kinetic processes rather than

by thermodynamic forces as in equilibrium segregation. Defect migration can

drive alloy microstructures either toward or away from equilibrium. The non-

equilibrium path is driven by radiation-induced segregation, which is caused by

the preferential transport of certain alloying components via persistent defect

f luxes generated during irradiation. Subsequent annealing at the same

temperature in the absence of irradiation will cause radia t ion- induced

segregation effects to diminish. In contrast, radiat ion-enhanced diffusion

results primarily from the random migration of the excess defects generated

during irradiation and hence, drives the system toward equilibrium.

Ion irradiation produces atomic displacements and hence, point defects, in

solids along the length of the ion track. At high temperatures, these defects are

240 G.S. WAS

mobile and are eliminated by mutual recombination or annihilation at sinks. If

either the production, annihilation or both are spatially inhomogeneous, net

defect fluxes will be induced. Since the motion of defects requires motion of the

atoms, e.g., vacancies exchange sites with neighboring atoms and interstitials

jump to neighboring interstices, defects will migrate preferentially by the

motions of atoms of one or more alloying elements. Thus, a preferential coupling

exists between defect fluxes and fluxes of certain alloying elements [58].

In order for radiation-induced segregation to occur, two conditions must exist

[58]: (1) a flux of defects into or out of certain spatial regions that persist in time

and (2) a preferential coupling of certain alloying elements to these fluxes. This

combination induces and maintains local concentration gradients that will decay

in the absence of defect fluxes. As a consequence, defect fluxes will

preferentially transport solute atoms into or out of local regions, causing

segregation. An important feature of defect-flux driven segregation is that

solute redistribution occurs regardless of the initial distribution of solute. This

redistribution has been studied most frequently in alloys in which the

components were homogeneously distributed throughout the material before

irradiation. However, significant effects have also been observed in the depth

distribution of implanted solutes [55] as well as in the distribution of solute

atoms introduced by ion-beam mixing of a thin surface layer [58].

As discussed by Wiedersich [58], the origins of persistent defect fluxes are

many. The most obvious cause for a defect flux into a spatial region is local

elimination of excess defects at sinks such as voids, dislocations, grain

boundaries, and surfaces. A less prominent cause for persistent defect fluxes is

defect trapping at local inhomogeneities such as solute clusters and coherent

interfaces that cannot act as independent defect sinks, but increase

recombination of vacancies and interstitials by virtue of trapping. Persistent

defect fluxes can also arise from non-uniform defect production. Since defect

production rates depend on composition, structure and bonding of the material

via the threshold displacement energy, defect fluxes may persist between

adjacent phases of different compositions and/or different structures. Finally,

non-uniform defect production is also a source of persistent defect fluxes.

During ion implantation, the defect production rate varies with the depth of the

bombarding particle, increasing to a peak at a location that is slightly shallower

than that of the implanted ion distribution, and then falling to zero just beyond

the end of range. The damage rate at the peak of the damage distribution can be

over an order of magnitude greater than that in the flat portion of the profile

near the surface. All of these inhomogeneities are sources for persistent defect

fluxes which contribute to radiation-induced segregation.


(i) Segregation mechanisms. Preferential coupling between alloying components

and the defect fluxes can occur by two mechanisms: inverse Kirkendall effects

and by the formation of mobile defect-solute complexes. These two mechanisms

couple a net flux of solute atoms to the defect fluxes, causing disproportionate

mass transport into and out of local regions, i.e., segregation. Significant defect

fluxes are produced during irradiation only when both types of defects, i.e.,

vacancy- and interstitial-types are mobile. Otherwise recombination dominates

and little long-range mass transport occurs. The temperature range in which

defect-flux driven segregation can produce redistribution of alloying components

over significant distances is about 0.3 to 0.5 of the absolute melting temperature.

(a) Inverse Kirkendall effect

Anthony [71] suggested that under irradiation, an "inverse" Kirkendall effect

can occur. Recall the Kirkendall effect in which a composition gradient can

induce a net flux of defects across a "marker" plane in an alloy. In the "inverse"

Kirkendall effect, defect fluxes would induce composit ional gradients in an

initially homogeneous alloy [72]. Under irradiation, both vacancy and interstitial

defects can produce inverse Kirkendall effects, Fig. 22 As shown in Fig. 22a, a

vacancy gradient near a sink in a binary alloy composed of elements A and B, generates a vacancy flux, toward the sink, which induces an atom flux (JAV+JB V)

of equal magnitude in the opposite direction, where JAv and JB v are the fluxes of

A and B atoms, respectively. Since JA v and JB v transport A and B atoms in

amounts proportional to their local atom fractions, C A and C B, and to their partial

diffusion coefficients, DAY and DBV, it follows that the alloy composition around

the sink does not change when DAV=DBV. However, if DAV=/DBv, the flux of the

faster diffusing component away from the sink will be proportionately greater

than its concentration in the alloy. Therefore, the inverse Kirkendall effect

induced by a vacancy flux will always cause depletion, at a sink of the faster diffusing component.

The same process holds for an interstitial ~'lux. However, because the interstitial flux and the complementary atom fluxes, JA i and JB i, move in the

same direction, Fig. 22b, any difference in the partial diffusion coefficients of the A and B atoms via interstitials, i.e. DAi g DBi will result in the preferential

transport of the faster diffusing component toward the sink. Therefore, depending on the relative magnitudes of the ratios DAV/DB v and DAi/DB i, the two

inverse Kirkendall effects may aid or oppose each other in causing solute segregation near a sink.

242 G.S. WAS

a

b

{~f,, -'I~C v

/ -,, ,,-h~" 4 o~, °B ~A

X~

/ -.--~ 2 : I ~ I B

o~cB

Fig. 22. Schematic illustration of inverse Kirkendall effects induced by (a) vacancy flux, and (b) interstitial flux. (from ref. 54)

X ~

a

c~

b

0 CA

~> nI

X ~

i nv o I ~A A -27 < ~-

J

Fig. 23. Effect of partial diffusion coefficients on the depth distribution of A atoms. (from ref. 54)

X ~


A simple treatment of RIS, proposed by Wiedersich et al. [56], is based on the

concept of partitioning the defect fluxes into those occurring by exchange with

the various alloy components and the atom fluxes, into those taking place via vacancies and interstitials. In a binary alloy AB, the fluxes of atoms, JA and JB,

and those defects, Jv and Ji, can be expressed in terms of the concentration

gradients of all species present as [57]

f~JA = -(DAv + DAi)VCA + DvAVCv - DiAvci, (3.49)

D.J B = -(DB v + DBi)VCB + DvBVCv - DiBVCi, (3.50)

~Jv = -(DvA + DvB)VCv + DAVVCA + DBVVCB, (3.51)

~Ji = -(Di A + DiB)VCi - DAiVCA - DBiVCB, (3.52)

w h e r e f~ is the average atomic volume and DAY, DA i, DvA, DiA are the partial

diffusion coefficients defined so that the subscript indicates the diffusing specie ,

and the superscript the complementary species via which the diffusion occurs. For example, DAY and DA i are the partial diffusion coefficients of A-atoms

migrating via vacancies and interstitials, respectively, and DvA and Di A are the

partial dif fusion coeff ic ients of vacancies and interst i t ials , respect ively ,

migrating via A-atoms.

In a concentrated binary alloy, Wiedersich et al. [56] derived the following

relation between the steady-state concentration gradient for the A component

and the vacancy concentration gradient:

VC A = (1/o0 DiBDiA/(DiBDA irr + DiADB irr) (DAV/DB v - DAi/DB i) VC v, (3.53)

DAirr and DBirr are the total radiation-enhanced diffusion coefficients for the A

and B atoms and t~ is a thermodynamic factor which deviates from unity for

non-ideal solutions. The two cases of interest predicted by eqn (3.53) are

illustrated in Fig. 23. Segregation of A away from the sink occurs when the

preferential transport of A atoms via vacancies exceeds that via interstitials.

Conversely, enrichment of A atoms at the sink occurs when the preferential

transport of A atoms by interstitials exceeds that via vacancies. The enrichment

of A at the sink is maximized when A atoms diffuse exclusively via interstitials

and B atoms via vacancies.

244 G.S. WAS

(b~ Defect-solute comolexes

In addition to the inverse Kirkendall effect caused by the different rates at

which defects exchange with atoms of different elements, defect-flux driven

segregation can also result from the formation of bound defect-solute complexes

[58]. An attractive interaction between point defects and solute atoms leads to a

preferential association, or defect-solute complex formation, which generally

affects not only the defect mobility but also the diffusion of substitutional solute

atoms. For example, a positive (attractive) binding energy between vacancies

and solute atoms increases the probability of a vacancy occupying a nearest-

neighbor site of a solute. Therefore, even in the absence of any changes in the

vacancy jump frequencies, binding affects the diffusivity of the solute atoms

differently than that of the solvent atoms. Similarly, formation of solute-

interstitial complexes will alter the diffusivi ty of the solute atoms via

interstitials. Furthermore, the defect jump frequencies will generally depend on

the proximity of solute atoms and their participation in the jump process. Hence,

effects of solute atoms on defect jump frequencies, and preferential solute-

defect association due to binding, cause a coupling between defect fluxes and solute fluxes.

These defect-solute complexes are especially important for segregation in

dilute alloys and have been extensively discussed by Johnson and Lam [49].

Defect-solute complexes can be considered to be mobile when the following relationship is satisfied:

' Ebd-S + Emd > Emd-S , (3.54)

that is, when the sum of the defect-solute binding energy, Ebd-S, and the defect

migration energy, Emd, exceeds the migration energy of the complex, Emd-S

Complexes that satisfy this condition may be regarded as distinct entities that

can migrate through the crystalline lattices. Since they flow in the same direction as the defect fluxes, both interstitial- and vacancy- type mobile

complexes will tend to sweep solute toward sinks in initially homogeneous alloys.

Defect-solute interactions are less effective at high temperatures and so are

expected to dominate at low temperatures while inverse Kirkendall effects may

dominate at high temperatures [66]. In the absence of intersti t ial-solute

interactions, solute enrichment at sinks can occur at low temperatures via

vacancy-solute complexes, and solute depletion at high temperatures due to the

vacancy-induced inverse Kirkendall effect. Calculations by Johnson and Lam

[49] show that binding energies of > 0.2 eV are required for mobile defect-solute


complexes to produce significant segregation. Only a few examples of vacancy-

solute binding energies of this magnitude have been reported in the literature,

but several well-documented examples of large (>0.5 eV) interstitial-solute binding energies exist [73]. As discussed by Okamoto and Wiedersich [48],

segregation by mobile interstitial-solute complexes is expected to be especially

important for undersize solutes since smaller atoms can be more easily be accommodated in interstitial sites.

The preferential participation of A atoms in the interstitial population can be

accounted for by incorporating into the diffusivity coefficients, factors that represent the fractions of A- and B-interstitials [56]:

CA i = CiC A exp(HAib/kT)/[CA exp(HAib/kT) + CB], (3.55)

CB i = CiCB/[C A exp(HAib/kT) + CB], (3.56)

where k is the Boltzmann constant, T is the absolute temperature, and HAl b is

the energy gained by converting a B-interstitial into an A-interstitial.

However, in order to account for atom transport by tightly-bound, mobile A

atom-vacancy (vA) complexes in dilute alloys, additional terms derived from the contribution of the complex flux JvA = -DvAVCvA must be included in eqns (3.49) and (3.51) for Jr, JA and JB:

t2Jv = [(DAV-DBV)O~ - KvADvACv]VC A - (D v + KvADvACA)VCv, (3.57)

~JA = - [tXDA + (1-2CA)KvADvACv]VCA-DiAVCi+[DvA-(1-2CA)KvADvACA]VCv, (3.58)

~JB = [etDB + 2CBKvADvACv]VCB - DiBVC i + [DvB + 2CB2DvADvA]VC v, (3.59)

where DvA is the diffusion coefficient of the vA complex, DvA = ~2VvAC/6 (nvA c being the complex jump frequency), and KvA = 12 exp(HvAb/kT) is the rate constant for the formation of vA complexes in equilibrium (HvA b being the

complex binding energy).

The idea of tightly bound solute-defect complexes migrating as distinct entities loses its well-defined meaning and its usefulness when the concentration of the solute exceeds a few atom percent [58]. For example, vacancies in

concentrated alloys will frequently have more than one solute atom as nearest

neighbors. Therefore, a multitude of vacancy-solute complexes containing d i f fe ren t numbers of solute atoms, many with several d is t inguishable configurations, would have to be considered. Furthermore, at high solute

246 G.S. WAS

concentrations, a vacancy jump may re-form a vacancy complex similar to that

existing prior to the jump, and 'complex migration' may occur without a

corresponding solute flux. Therefore, Weidersich et al. [56] used the formalism

described in section 3.E.i to arrive at eqn. (3.53) for the relation between

concentration gradients of solute and defects in concentrated alloys.

With regard to intersti t ials, however, there exists both experimental

[54,74,75] and theoretical evidence [76] which supports the formation of tightly

bound solute-interstitial complexes for undersized solutes, in both the dilute and

concentrated limits, which migrate as solute interstitials. Hence, Wiedersich's

model for segregation appears well suited to describe alloy systems with

significant atomic size differences, including the limit in which the undersized

component is present in dilute solution. The origin of the size effect follows.

(ii~ Solute size effect. The size difference between solute and solvent atoms

plays a strong role in the magnitude and direction of radiation-induced

segregation through the reduction of the strain energy stored in the lattice [51].

This provides the driving force for the undersize solute substitutional atoms to

preferentially exchange with solvent atoms in interstitial positions, whereas

oversize solute atoms will tend to remain on, or return to, substitutional sites.

The same strain-energy considerations will drive vacancies to preferentially

exchange with oversize solute atoms. During irradiat ion at elevated

temperature, the fraction of undersize solute atoms migrating as interstitials, or

of oversize solute atoms migrating against the vacancy flux, may greatly exceed

the fraction of solute in the alloy. Such a disproportionate participation of

misfitting solute atoms in the defect fluxes to sinks will cause a redistribution of

solute, which will produce an enrichment of undersize solute and a depletion of

oversize solute near defect sinks. Since the surface of an irradiated solid serves

as an unsaturable link for both defect types, concentration gradients will be

created near the surface of alloys that contain misfitting solute atoms during

irradiation at appropriate temperatures.

Irradiation of solid solution binary alloys of 1 at% AI, Ti, Mo and Si in Ni with

3.5 MeV Ni + ions produced sharp concentration gradients near the irradiated

surface in all the alloys [51]. The three oversize solutes, AI, Ti and Mo with misfits of +0.05, +0.10, +0.12 (where misfit is defined as the fractional change in

lattice parameter of a solid-solution alloy produced per atom fraction of solute,

{Aa/a}/c), all exhibited depletion from the irradiated surface and an enriched

region at intermediate depths, Fig. 24a-c. The undersize Si, however, shows

enrichment at the irradiated surface followed by depletion at intermediate


depths, Fig. 24d. In fact, Table 2.1 shows some 26 binary alloys in which RIS has been observed along with the corresponding volume misfit [61]. As shown, there are only three discrepancies with theoretical predictions.

I 0

T I ]

N i - I AI

J I I I 0 0 2 0 0 3 0 0

Oepth (rim)

(a)

I I I

5 7 5 ° C

i N i - I Ti

1 _ _ 50 I0~0 I / 0

Depth (nm)

(b)

2 0

15

%

.9

<

z

5

I I T

®

615°C

Ni - I MO

0 - - 510 I010 i / 0

Depth (nm)

SO

zo

io

® - 8 5 dpe o~ 560"C 9~ 39 dpo ot 600"C • - 4 4 apo o~ 660"C

o ~oo zoo

(c) (d)

Fig. 24. Measured concentration vs depth profiles for a (a) Ni-1 at% A1 alloy irradiated to 10.3 dpa at 510°C and 10.7 dpa at 620°C, (b) Ni-1 at% Ti alloy irradiated to 11.2 dpa at 515°C and 8.5 dpa at 575°C, (c) Ni-1 at% Mo alloy irradiated to 11.6 dpa at 530°C and 11.2 dpa at 615°C, and (d) Ni-1 at% Si alloy irradiated to 8.5 dpa at 560°C, 3.9 dpa at 600°C and 4.4 dpa at 660°C. (ref. 51)

248 G.S. WAS

T a b l e 1. V o l u m e m i s f i t p a r a m e t e r s b a s e d on a t o m i c s i z e or m e a n a t o m i c v o l u m e d e t e r m i n e d fo r a n u m b e r o f s o l u t e / s o l v e n t s y s t e m s . N o t e tha t the d i s c r e p a n c i e s in the

d i r e c t i o n o f s e g r e g a t i o n ( u n d e r R I S ) p r e d i c t e d f rom the K i n g v o l u m e m i s f i t p a r a m e t e r [67]

are r e m o v e d w h e n the a t o m i c s i ze v o l u m e m i s f i t p a r a m e t e r i s used . ( f rom ref. 66)

rsolv(./~) S t r u c t u r e Al loy rsol(,/~) Structure Volume Direction Volume of the solute misfit % of misfit %

when (rsol /rsolv) 3- 1 s e g r e g a t i o n after King c r y s t a l l i n e [62] [671

1.3775 fc c

1.4315 fcc

1.278 fcc

1.2458 fc c

1.4478 h c p

1.24115 bcc

1.59855 h c p

Pd-Cu 1.278 fcc -20 + -19 Pd-Fe 1.24115 bcc -27 + -12 Pd-Mo 1.36255 bcc -3 + Pd-Ni 1.2458 fcc -26 + -14 Pd-W 1.37095 bcc -2 + -4

AI-Ge 1.2249 d i amond -37 + +13 AI-Si 1.17585 d i amond -45 + -16 A1-Zn 1.3347 h c p -19 + -6

Cu-Ag 1.4447 fcc +44 +44 Cu-Be 1.1130 h c p -34 + -26 Cu-Fe 2.24115 bcc -8 + +5 Cu-Ni 1.2458 fcc -7 + -8

Ni-A1 1.4315 fcc +52 +15 Ni-Au 1.44205 fc c +55 +64 Ni-Be 1.1130 h c p -29 + <0 Ni-Cr 1.2490 bcc +1 +I0 Ni-Ge 1.2249 d iamond -5 + +15 Ni -Mn 1.36555 fcc (3,-phase) +32 +23 Ni-Mo 1.36255 bcc +31 +22 Ni-Si 1.450 r h o m b o h . +58 +21 Ni-Si 1.17585 d iamond -16 + -6 Ni-Ti 1.4478 h c p +57 +29

Ti-AI 1.4315 fcc -3 + -20 Ti-V 1.3112 fcc -26 + -15

Fe-Cr 1.2490 bcc +2 +4

Mg-Cd 1.4894 hcp -19 + -21


Ciii) Dose dependence. The dose dependence of RIS has been measured by

Averback et al. [63] in a Ni-12.7 at% Si alloy bombarded with 2 MeV He + ions.

Since the external surface serves as a sink, the preferential transport of silicon

by the defect fluxes causes the silicon concentration at the surface to exceed the solubility limit of -10 at% and a coating of Ni3Si (7') forms. The thickness of the

layer grows with increasing dose and the slope of the growth rate curve is the

growth rate constant. The data shown in Fig. 25 for irradiation with 2 MeV Li7

at 520°C give a coating growth that is parabolic with time. That is, at a constant

dose rate, the coating thickness is proportional to the square root of the dose.

The dose dependence is also shown more qualitatively [64] in Fig. 26. The dose

dependence of RIS to the surface has also been investigated in three other alloy

systems; Cu-Ni, Ni-Ge and Ni-Sb. In all three cases, growth of the segregated

surface layer was found to be approximately parabolic with dose [72].

80

60

~. 40

I I I t _ 2 MeV 7Li+ 520"C d / _

[ I I I 0.5 1.0 1.5 2.0 2.5

(DOSE)1/2 (dpal/Z)

Fig. 25. Thickness of the y' surface layer as a function of the square root of dose for 2.0 MeV Li irradiation at 520°C and a dose rate, Ko of 4 x 10 -4 dpa/s. (from ref. 63)

(iv~ Temperature d~pendence. The temperature dependence of radiation-

induced segregation results from the interplay of several factors. At low

temperatures at which the i r radia t ion-produced vacancies are re la t ively

immobile, the recombination rate of vacancies and interstitials will be high. This

greatly reduces the fraction of defects that annihilates at sinks and consequently

the degree of radiation-induced segregation. At high temperatures, enhanced

recombination that results from the larger equilibrium vacancy concentration,

25O G.S. WAS

faster back diffusion and the decreased effectiveness of defect-solute binding

combine to again inhibit segregation. However, at intermediate temperatures (typically 0.3 to 0.5 Tm), significant solute participation in the defect fluxes may

occur, resulting in pronounced solute segregation over large distances (10s to

100s of nanometers). The temperature dependence of radiat ion-induced

segregat ion is therefore expected to closely resemble the temperature

dependence of the radiation-enhanced portion of the diffusion coefficient.

6 0

50 '

!

i 40

_o

,,=, 3 0

Z

2C

T l ~ - I

Ni - I At. % Si

• 6.5 dpo AT 522~C o 2.8 dpo AT 525:C o 1.0 dpo AT 516"C o O. 16 dpo AT 537"C ~' 0.05 dpo AT 535*C

--15

!

i --~-- ~UT. I

0 tO 20 30 40

DEPTH (nm)

25

Fig. 26. Si/Ni peak-to-peak ratios as a function of depth from the irradiated surface for a series of Ni-1 at% Si alloys irradiated to different doses at a minimal temperature of 525°C. The right ordinate gives Si/Ni peak-to-peak ratios obtained from unirradiated Ni-Si alloys of known Si concentration. (from ref. 64)

The temperature dependence of RIS has been studied by many investigators.

Rehn et al. [51] studied the dependence of Si segregation on irradiation temperature in a Ni-1 at% Si alloy bombarded with 3.5 MeV Ni + ions, and

Averback et al. [63] studied the same dependence in a Ni-12.7 at% Si alloy

during 2 MeV He + bombardment. Since the external surface curves as a sink, the

preferential transport of silicon by the defect fluxes causes the silicon

concentration at the surface to exceed the solubility limit of -10 at% and a

ION BEAM MODIF ICATION OF METALS 251

coating of Ni3Si (7') forms. The thickness of the layer grows with increasing dose

and the slope of the growth rate curve is the growth rate constant. When

plotted as a function of temperature, Fig. 27, the peak in the growth rate occurs

at an intermediate temperature as expected from theory. At low temperature

the growth rate is low due to the high recombination rate of vacancies and

interstitials resulting from the high excess vacancy concentration due to the low

vacancy mobility. At high temperature the growth rate also diminishes due to

the increase in the equilibrium vacancy concentration and thus, recombination.

But at intermediate temperatures, the segregation peaks. The same is true for

irradiation of Ni- la t% Si, Fig. 28. Several others have investigated the

temperature behavior of RIS and found the same qualitative dependence [51,55].

T ( ~ ) 650 550 450 ~$0

I [ [ I

.,- E~.,.2.v g

w

Ni* 1 2 . 7 0 /o $i / o

2 MIIV 4He I 1

3.1 • I0 -4 d l l / I

- J I ~ I 1 " I.O 1,2 1.4 I .G

T - I ( i0 ~ K - j )

Fig. 27. Arrhenius plot of the measured growth rates of T'-coatings on Ni-12.7at% Si specimens during 2 MeV He 4 bombardment at a dose rate of 3.1 x 10 -4 dpa/s (4.7 x 1014 ions/cm2-s). (from ref. 62)

{ ~ C Y I 3 . 5 - - M e V Ni ON O 0 3 ~ j ~ I Ni--I */o o, Si

o I~ I oso,po,38s°c II~ I o 4.o ~0o,~o°~ l ~ 1 o~.~ ~ , ~ o ° o

° ° ~ 1 1 f I ~ ~,~oooc • 4 4 d p o , 6 6 0 * C

°

o T o T o 5oo ~ooo tsoo

DEPTH I~)

Fig. 28. Si/Ni peak-to-peak ratios versus depth from the irradiated surface for a series of Ni-1 at% Si a l l o y s i r r a d i a t e d at v a r i o u s temperatures and doses. A Si/Ni ratio of 0.033 corresponds to 25 at% Si. (from ref. 51)

(v) Dose rate effect, The magnitudes of the defect fluxes, which determine the

degree of radiation-induced segregation near sinks, are temperature and dose

rate dependent. Since the minimum in the defect recombination rate shifts

toward lower temperatures for lower damage rates, decreasing the defect

production rate is expected to decrease the temperature where maximum

segregation occurs. Current theory also predicts that the RIS growth rate

constant should vary inversely as the fourth root of the dose-rate in the

recomibina t ion- l imi ted temperature regime [62]. Averback et al. [63] also

252 G.S. WAS

investigated the dose rate effect on the radiation-induced formation of Ni3Si, Fig.

29. The predicted fourth-root dependence in the recombination-limited regime is indicated by the dotted line. The observed dependence of the RIS rate on dose-rate is sl ightly weaker than predicted, but the agreement is considered reasonable. Since the vacancy concentration during irradiat ion at high

temperatures is approximately equal to the equil ibrium vacancy concentration, the amount of defect annihilation per unit dose is independent of dose-rate, and and no effect of the dose-rate on the growth rate constant is predicted at high temperatures. As can be seen from Fig. 29, the experimental results support this conclusion in the case of Ni-12.7 at% Si.

50

, N

o

10

T ('CI

7 ~ 6OO 500 4OO 350 _1 ' 1 I I ' I I

O

I -'-i • •

Ni- 12.7 Olo Si 2 MeV 4He • 3.11 iO -4 dpo/s 0 2.6x 10-5 dpo/s

21 j I i t t I 1.0 1.2 1.4 1.6

T -~ tlO "3 K-q

Fig. 29. Arrhenius plot of the growth-rate constant for two dose rates 3.1 x 10 -4 dpa/s (closed symbols) and 2.6 x 10 -5 dpa/s (open symbols). (from ref. 63)

The dependence of RIS on dose rate in Ni-10 at% Ge has also been studied [77].

RBS measurements clearly show that during irradiation with 2 MeV He + at

450°C, more Ge is transported to the surface at a dose rate of 2.6 x 10-5 dpa/s

than at 3.2 x 10 -4 dpa/s over a range (0.04-1.0 dpa) of total doses. These results

are in qualitative agreement with those for Ni-Si.


(vi) Homogeneous alloys. Some very striking examples of solute redistribution by RIS have been observed by Robrock and Okamoto and reported by Rehn and

Wiedersich [72]. In the case of a Ni-6 at% Si, single phase, solid solution alloy

irradiated with MeV ions, the defect generation rate does not vary strongly with

depth over the first few hundred nanometers. At these shallow depths of

penetration, the surface serves as the dominant sink. Silicon is preferentially

transported to the surface until the solubility limit (10 at%) is exceeded, where upon Ni3Si (y') begins to precipitate. As silicon is transported to the surface from

the interior, the layer thickness grows until the effectiveness of the sink

diminishes relative to internal sinks. Then, precipitation begins to occur at these sinks with the same result. Voids, dislocation loops and grain boundaries all

become coated with y'. Hence, RIS has decomposed a single phase alloy into a

two-phase material.

A similar spatial redis t r ibut ion occurs when the solute atoms are

preferentially transported away from sinks. The result is an enrichment in solute a distance away from the sink. If the matrix composition is close to the

solubility limit, precipitation may occur in these regions (since they are usually rather large compared to the solute depleted regions and only small changes in

composition are expected) and the solid solution alloy is decomposed into a two-

phase structure. RIS in two-phase alloys can redistribute the phases by solute redistribution.

Thermally aged Ni-AI alloys result in a uniform distribution of cuboidal Ni3A1

0/') particles. During irradiation, aluminum depletion shifts the local composition

around sinks into the solid solution range [78], Precipitate-denuded zones form

at the surface and around internal sinks such as dislocation loops, and ~/' becomes concentrated in the sink-free areas.

(viD Damage distribution ~nd bombarding ion effects. When the rate of defect product ion during irradiat ion varies with ion depth, rad ia t ion- induced segregation, which is driven by gradients in the point-defect concentration, Cd,

can become significant. Early in the irradiation, the composition of the alloy is still fairly uniform and the flux, JA, of element A is essentially proportional to V C d. From the diffusion equation,

3CA/~t = -VJ A, (3.60)

it follows that the divergence of the defect flux, ~72Cd, is therefore a measure of

the rate of accumulation of solute at a given depth. Examples of the variation in

254 G.S. WAS

E o, C d, dCd/dX, and d2Cd/dX2 with distance from the free surface are shown in

Figs. 30 and 3] for low- and high-energy ions, respectively [?2]. Note that positive values of d2Cd/dx2 will cause solute accumulation if the solute and

defect fluxes move in the same direction, but solute depletion if the fluxes are in

opposite directions. By this reasoning it can be seen that these examples are

representative of solute redistribution via the interstitial inverse Kirkendall

effect. In these cases, solute enrichment will occur in regions along the ion range where the defect profile is concave upward, while regions that are concave

downward will be depleted of solute. In both the low- and high-energy cases, solute enrichment occurs at the bombarded surface and just beyond the damage

peak, while the peak and near surface regions are depleted of solute. A

difference between the high- and low-energy ion bombardment occurs in the midrange region, about halfway between the damage peak and the surface,

where solute enrichment occurs for high-energy ions but not for low energy ions.

x, ~ (a)

(b}

I (c) I

dca I

I L (d)

Rp

K o

dC d

a2Ca

j ~ bl

I I

___ I I (c) I

I I I I d

7 IRP

Fig. 30. Schematic plots of (a) defect production rate Ko, (b) steady-state defect concentration Cd, (c) dCd/dx, and (d) d2Cd/dx 2 versus depth for low-energy ions. (from ref. 72)

Fig. 31. Schematic plots of (a) defect production rate Ko, (b) steady-state defect concentration Cd, (c) dCd/dx, and (d) d2Cd/dx 2 versus depth for high-energy ions. (from ref. 72)

I O N B E A M M O D I F I C A T I O N O F M E T A L S 2 5 5

In addition to differences in solute redistribution due to ion energies, the mass of the ion can significantly affect the degree of radiation induced segregation

[72]. This is due to the variation in the efficiency for producing freely migrating

defects (which fuels RIS) with ion type. Figure 32 shows the relative efficiencies (normalized to that of 1 MeV protons) for defect production as a function of the defect-product ion weighted-average recoil energy, PI/2. Pl/2 is the primary

recoil energy above and below which half of the defects are produced. It gives a measure of the spatial distribution of the defect production; the larger the value of Pl/2, the greater is the tendency for defects to be produced in cascades rather

than as isolated defects. This figure provides a quantitative representation of

the relat ive e f f i c iency for producing solute redis t r ibut ion at e levated

temperatures as a function of the hardness of the primary recoil spectrum.

Qualitatively, as recoil events increase in energy from tens to hundreds of electron volts, Frenkel pair production changes from the introduction of randomly distributed isolated Frenkel defects to the generation of defect pairs in

close proximity. Cascade regions form for primary recoil energies above 1 keV.

Hence, since RIS is tied to the efficiency of defect production, the degree of the

observed segregation can be expected to vary substantially depending upon the ion and the energy used during the irradiation.

1.0

°~ o.8

0.6 ~J

0.4

~ 0 2

0 i0 2

I I 1 r - - ~IMeV H

\ Q~2 MeV He

NeV Li

~ . 5 MeV Ni

I I " ~ r T 3.25 MeVKr

,o ~ ,o" ,o ~ ,o ~ ,o' Pr/2 (eV)

F ! !

=-

!

' I ' I ' I

/ / '

~ ' \~",~

r •

, I , I ~ I 1.2 1.4 1.6

T ' l l io$ K - I )

Fig. 32. Relative eff iciencies of various ions for producing long-range m i g r a t i n g d e f e c t s at e l e v a t e d temperature plotted as a function of the weighted-average recoil energy. (from ref. 72)

Fig. 33. Arrhenius plot of the growth rates of? ' coatings on Ni-12.7 at% Si specimens for different ions. The calculated displacement rates were kept approximately constant at 3 x 10 -4 dpa/s. (from ref. 62)

256 G.S. WAS

A large reduction in the growth rate of ~' coatings on Ni-12.7 at% Si alloy, with

ion mass was observed by Rehn [62] while keeping the near-surface

displacement rate constant for all ion masses, Fig. 33. In this case, it was found

that sinks produced by the heavier ion bombardment significantly reduced RIS

to the surface at 485°C. However, experimental evidence also shows that defect

losses within the denser cascades also contributed to the reduction in RIS.

F. Gibbsian adsormion

The readjustment of the surface composition of a homogeneous alloy to a

composition different than that in the bulk, in an effort to minimize the free

energy of the system, is known as Gibbsian adsorption (GA) [79]. Also known as

thermal surface segregation, this process can lead to substantial changes in

composition in the first one or two atom layers at the surface, while leaving the

bulk composition practically unaffected due to the large bulk-to-surface-volume

ratio. The readjustment occurs spontaneously at temperatures sufficiently high

for diffusion to proceed at reasonable speed. At equilibrium, the atom fractions of A and B in the "surface phase", CAS and CB s, are related to the respective atom

fractions in the "bulk phase", CA b and CB b, by the relationship [79]

CAS/CB s = (CAb/CB b) exp (-AGa/kT), (3.61)

where AG a = AH a - TAS a is the GA free energy, with AS a and AH a being the

entropy and enthalpy of adsorption for the A component, respectively.

During the concentration buildup towards equilibrium, the net flux of A atoms into the surface atomic plane, JA, is calculated by [80]

~JA = (VAb->SCAbCB s - VAS->bCASCBb)~, (3.62)

where ~ is the atomic layer thickness, and the surface-to-bulk jump frequency VAS->b is related to the bulk-to-surface jump frequency vAb->s by the following

equation based on the condition of equilibrium (JA = 0)

VAS->b = vAb->s exp (AGa/kT). (3.63)


Since vAb->s is a function of defect jump frequencies by exchange with A atoms

and defect concentrations in the bulk, then

vAb->s = VAvCv b + VAiCi b, (3.64)

and GA can be strongly enhanced by irradiation at temperatures below -0.6T m.

The dependence of Gibbsian adsorption on temperature has recently been measured on a number of alloys [81-83] using ion scattering spectroscopy, and the 1/T dependence of In[CAS/CBS], from eqn. (3.63), has been confirmed for Ni-

Cu and Ni-An alloys [81,82]. Gibbsian adsorption involves compositional changes in the first one or two

atom layers, which is a comparable depth scale to the effects of preferential

sputtering. Hence, under ion bombardment, the surface composition will be affected by both of these processes. Lam and Wiedersich [80] provided a

schematic description of the dynamic behavior of the surface composition during

ion bombardment resulting from the simultaneous effects of GA and PS. In this example, Fig. 34, Gibbsian adsorption results in a surface concentration of A

atoms that is initially greater than the bulk level. This leads to enhanced

preferential sputtering of A atoms since the sputtered atom flux is primarily

from the first atom layer. Consequently, the concentration of A atoms in the subsurface layer will be significantly reduced in an effort to re-establish

thermodynamic equilibrium. However, at steady state, the composition of the

sputtered atom flux is equal to the bulk composition of the alloy.

C a

%\ t I t 3 14

C A OF SPUTTEREO-ATOM FLUX

\ I I L_ _l_~_ ~- ,~ 2 __--_ _ - - , c:"--'

_ _ - - - - _ _ C ( A I ~ - -

I ~ ~ = CONCENTRATION

~1 82 ~3 ~4 DEPTH x

Fig. 34. Schematic description of the simultaneous effects of GA and PS on the time evolution of the sputtered-atom flux composition and alloy composition in the near surface region. (from ref. 80)

258

G, Soutterin~ v

G.S. WAS

(i~ Basic model. Sputtering is a key element in determining surface composition

under ion bombardment, primarily through the action of preferential sputtering.

However, all of the processes discussed thus far will contribute to the observed

effects. Since different elements sputter with different probabilities, and the

surface composition is a function of this probability as well as the processes of

ion implantation, displacement mixing, radiation-enhanced diffusion, radiation-

induced segregation and Gibbisan adsorption, the resulting surface composition

will also depend on these processes. This section will briefly describe the

process of physical sputtering, followed by a discussion of preferential

sputtering as it affects surface compositional changes in alloys.

S i g m u n d [84-86] developed the basic theory and description for the sputter

yield due to linear cascade sputtering, and Winters [87] provided a clear and

concise summary of theory and experiment. Linear cascade sputtering refers to

conditions on the collision cascade. A collision cascade is linear if only a minor

fraction of the target atoms within the cascade volume is set in motion. For a

bulk cascade, this implies a low density of point defects generated. As applied to

sputtering, it means that the sputter yield must be small compared to the

number of target atoms located within the surface area affected by a

bombarding particle. In practice, cascades in metals are close to linear except

those generated by rather heavy ions bombarding heavy targets in the energy

range from ~10 keV to -1 MeV. The linear sputter yield formula is

Y = AF D, (3.65)

where Y is the number of atoms emitted per incident particle, L contains all the material properties and incident ion angular dependence and F D is the density of

deposited energy per unit depth at the surface and depends on the type, energy and direction of the incident ion and the target parameters Z 2, M 2 and N. The

derivation of A involves a description of the number of recoil atoms that can

overcome the surface barrier and escape from the solid. Sigmund [84] has

derived an expression for A using the Thomas-Fermi screening function

A = 0.042/NU o, (3.66)

where N is the atomic number density and U o is the surface binding energy and

can be estimated from the heat of sublimation. The deposited energy F D is given

a s


F D = ctNSn(E),

259

(3.67)

where a is a dimensionless quantity depending on the relative masses and angle of incidence [84], and Sn(E) is the nuclear stopping power. For keV energies and

heavy-to-medium mass ions, the expression for the nuclear stopping power is

calculated by Lindhard [10,88], using a Thomas-Fermi cross section [89],

Sn(E ) = 41tZ1Z2e2a[MI/(Ml+M2)]Sn(e), (3.68)

where Sn(¢) is the reduced stopping power, a is the screening radius, Z1, M1 and Z2, M 2 are the atomic numbers and masses of incident ion and target atom,

respectively, and

e = aM2E/[Z1Z2e2(MI+M2)]. (3.69)

The sputtering yield is therefore

Y = 0.528ct Z lZ 2 M1/[MI+M 2] Sn(e)/U o. (3.70)

This model has undergone extensive experimental testing and has enjoyed

considerable success. However, systematic deviations have been pointed out for some cases such as light-ion sputtering and low-energy sputtering. Current theories are summarized by Mashkova and Molchanov [90]. Yamamura et al.

[91] have proposed a new empirical formulation of the sputtering yield to

account for both light-ion and low-energy sputtering in the sputtering yield.

Kelly, Falcone and Oliva have undertaken a full re-examination of collisional

sputtering theory. In this re-analysis, they have addressed the treatment of the collision cross section [92], the surface binding energy [93], the scaling of

deposited energy [94], the characteristic depth and cross section for low-energy

elastic collisions [95], the effect of crystallinity [96] and preferential sputtering

effects [97]. It is not the intention of this paper to discuss basic sputtering theory, but rather the means by which sputtering influences the composition of

bombarded surfaces. With these formulations in hand, we can now discuss the effect of sputtering on compositional changes in the target.

(ii) Preferential sputtering. Wiedersich et al. [98], proposed a simple concept and definition of preferential sputtering by writing the yield or number of A-

260 G.S. WAS

atoms of an alloy per incident ion in the flux of sputtered atoms as

7 YA = J oA(x) (CA(X)/fl)dx, (3.71 )

0

where OA(X) is the cross section for A-atoms at a depth x>0 to be ejected from

the surface, x=0, into the region x<0 per incoming ion, CA(X) is the atomic fraction

of A in the alloy at depth x, and fl is the mean atomic volume. He then goes on to define PA(X) = OA(X)/f~, where pA(x) is the probability per unit depth that an

A-atom present at depth x is ejected by an incoming ion. The yield of A-atoms

then takes the form

o o

YA = f pA(x) (CA(x)dx, (3.72) 0

In this form, the distinction introduced by Sigmund [99], between the primary

and secondary effects in alloy sputtering is made explicit. The primary effects

are those related to the individual sputtering events and the physical variables contributing to the sputter yield are all contained in the sputter probability, PA,

which depends on the type and energy of the incoming ion, the type of the

sputtered atom and its surface binding energy, etc. Since the values of the sputter probabil i t ies, Pi, will differ for differing atomic species, preferential

sputtering will occur.

The secondary effects in alloy sputtering enter into eqn. (3.72) via the atomic concentration, CA, which gives the probability that a site is occupied by an A-

atom. All processes mentioned earlier that affect the surface composition during

bombardment, eg., recoil implantation, Gibbsian adsorption, RIS, etc., but not

preferential sputtering, enter primarily through their effects on the near-surface

concentration. As a consequence, the sputter yields of the alloying components will be affected through the factor CA(X) in eqn. (3.72).

Practically, since sputtered atoms come from a shallow layer as shown by

Sigmund [84,85], and later by Falcone and Sigmund [100] the integral in eqn

(3.72) can be replaced by

YA - pACA s • (3.73)

where PA is the average total probability for an A-atom present in the surface

layer to be sputtered off per incident ion and CA S is the average atomic

concentration of A in the surface layer. The thickness of this layer is not well defined but should be taken as one or two atomic layers for determining CAS


since the origin of sputtered ions is heavily weighted toward the first atomic

layer. Differences in the sputter probabilities for component atoms in an alloy are

caused by differences in the amounts of energy and momentum transferred to

atoms of different masses, and surface binding energies. However, continued

sputtering of a semi-infinite alloy target of uniform bulk composit ion must

eventually lead to a steady state in which the composit ion of the flux of

sputtered atoms leaving the surface equals the composition of the bulk alloy.

Lam and Wiedersich [80] have shown that bombardment of a binary alloy AB

with a flux of ions ~ ( ions/cm2s) leads to an atom removal rate given by

dN/dt = ~(YA + YB)- (3.74)

Therefore, the rate at which the sputtered surface recedes can be calculated

from the total rate of atom loss per unit area,

= dS/dt = ~f~ dN/dt = ~f~(PACA s + pBCBS), (3.75)

where ~ is the thickness of the surface layer removed by sputtering.

fl t 2 13 14 I J

I / C A OF SPUTTERED-ATOM FLUX

-.,-.... ~ ~ ' - - ' - - - _ - - _C& built

C(I)

J PROFILE

8 2 8 5 8 4 DEPTH •

Fig. 35. Schematic description of the preferential sputtering effect on the time evolution of the composition of the sputtered-atom flux and of the near-surface region in the alloy. (from ref. 80)

Lam and Wiedersich [80] have described the time evolution of PS on the near- surface composition for a binary alloy AB with ~"~s > p"~s, i.e. for the case where

PS of A atoms occurs, Fig. 35. Note that initially, the concentration of A atoms in

the sputtered flux is larger than in the bulk. However , as the surface

262 G.S. WAS

composition changes and the near-surface layer composition is altered, a steady

state will be achieved after a certain bombardment time, when the composition

of the sputtered-atom flux becomes equal to the bulk composition, as dictated by

the law of conservation of matter. At steady state, the following condition must

be fulfilled,

YI :Y2:Y3 . . . . Clb:C2b:C3 b .... (3.76)

that is, the ratios of the alloy components in the sputtered flux are the same as

those of the bulk alloy and their concentrations are just uniformly diluted by the

reemitted sputter ions. Combining this result with eqn. (3.73) the ratio of the

total sputter probabilities is

Pl:P2: . . . . . (Clb/ClS):(C2b/C2s): ..... (3.77)

i.e., after steady state is attained, the sputter probabilities are proportional to

the ratio of the bulk and surface concentrations of the element in question.

H. Phenomenological model for surface comoosition changes

Accounting for the effects of all the processes described in the previous

sections, Lam & Wiedersich [80] constructed a phenomenological model for

bombardment-induced composition modification by formulating a set of coupled

partial differential equations describing the temporal and spatial evaluation of

defect and atom concentrations during ion bombardment of a binary alloy. The

formulation was based on the set of diffusion and reaction rate equations, i.e.,

Fick's second law with source and sink terms, describing the time-rate of change

of the alloy composition and defect concentrations,

3Cv/bt= - V.(f2Jv) + K o - R, (3.78)

bCv/bt = - V.(f2Ji) + K o - R, (3.79)

3CA/~t = -V.[(f2Jh) - DAdisp VCA], (3.80)

where K o and R are the local, spatially dependent rates of production and

recombination of vacancies and interstitials and DAdisp is the diffusion coefficient


caused solely by the displacement process. The time-dependent atom and defect

concentration distributions can be determined by solving eqns (3.78) through

(3.80) numerically for a semi-infinite target using appropriate starting and boundary conditions as described by Lam [80,101,102]. This formulation covers

the processes of DM, RED and RIS. Gibbsian adsorption and preferential

sputtering can be accommodated in the model by treating the surface layer as a

separate phase. Because of the structure of the phenomenological model,

calculations can be made to determine the dependence of surface and subsurface

compositional changes on material and irradiation variables as well as isolating

the contributions of individual processes. However , because many of the

parameters needed in the models are unknown, quantitative comparisons with

exper iment are di f f icul t . Never the less , semiquant i ta t ive model ing of

bombardment- induced composi t ional redistr ibution in several binary alloys

have been made.

Lam and Wiedersich [80] calculated the composition distributions in a Ni-40

at% Cu alloy bombarded with 3 keV Ni + at 500°C. Figure 36 shows the spatial

distribution of Cu atoms for a number of sputtering times. The calculated peak

damage rate was 3.5 x 10 -2 dpa/s and corresponds to an ion flux of 3.75 x 1013

/cm2s. The peak damage occurs at a depth of - lnm. The projected range is ~7

nm and the spatially dependent damage rate is shown by the dashed curve in

the to graph for time t=0. The thickness of the surface layer removed by

sputtering is indicated for various times. Since the initial starting conditions

correspond to the thermodynamic equilibrium state of the alloy, with an

equil ibrated Cu enrichment due to GA at the surface, the Cu surface concentration, CCu s is very high initially, then decreases with sputtering time,

and finally attains a steady state value after ~104 s.

The temperature dependence of the bombardment- induced composi t ional changes as measured by the time evolution of CCu s and the steady state

concentration profiles is shown in Fig. 37. At short sputtering times, t< 10 s, GA controls the magnitude of CCu s, when starting from the equilibrium state, at

which CCu s is nearly 100 at%, Fig 37a. With increasing time, however, PS and RIS

lead to a gradual decrease in CCu s towards a steady state value. At steady state,

the surface alloy composi t ion, CCuS/CNi s, is determined by the relative

contributions of the first and second layers to the sjguttered atom flux and the

bulk composition, in such a way that the compositions of the sputtered atom flux and the bulk alloy become equal.

264 G.S. WAS

08 . 6 0

20 o L . . . . . . . . . . . . . . . . . o2 0 0 2 IO ° IO I IO '?" ~0 ~

h l l

4 ° 20

0 , ,,i , , . . . . . . . , , ,,i 0 0 2 10° iO I 102 103 g~3 _ ~ ~ ,.~o,

3 - WIV N I *

(~ T • 5OO'C

I ,.3r~,,o, Kn',Ol, 14 K

' " ^ ' ' ' ' J . . . . ' Z . . . . " o Z I O ' ° Z ~(3 ~ I 0 ~ I0 IC ~

~ ! : 0~ komlO0 ~ . . f , 1021

§ ,, . . . . . . I 20

, Oo.~ ~o ; ~ j , ~;L,

tOOl- ~. ~ 0 % l ill ~ ~ w ~ O ( ItlodY itot*)

ORIGINAL SURFACE

ql r;, . . . . . . . . . 1 . . . . i . , , , j O Q 2 IO O t

926 4 rim

IO* =O 'z K:P

N=*O~ N~-40 ol % C.

• 375 • IO 13 ~ s / ¢ ~ ' • 14 KIO -2 dco/s

DISTANCE F R O M S U R F A C E ( r i m )

Fig. 36. Calculated time evolution of Cu concentration profiles in a Ni-40 at% Cu alloy sputtered with 3-keV Ne + ions at 500°C. The profile of the damage rate Ko is shown by the dashed curve in the top portion, and the thickness of the surface layer removed by sputtering is indicated. The energies for vacancy migration via Cu and Ni atoms were taken to be 0.95 and 0.97 eV, respectively. (from ref. 8 0 )

Figure 37b shows the steady state concentration profiles in the subsurface region calculated for various temperatures. Near room temperature, where point-defect mobility is limited, PS and DM are the main processes that govern the development of the alloy composition in the altered layer, which extends to a depth approximately equal to the damage range. The additional effect of GA, which is quite small at this temperature, is reflected by the noticeable difference between CCu s in layers 1 and 2. Above ~100°C, GA, RED and RIS become

significant, and effectively determine the extent of and the composition in the altered layer. The higher the temperature, the thicker the altered layer. At 700°C, the thickness of this layer is ~4 ~tm, which is - 600 times larger than the damage range. Compositional changes at such large depths suggest that the effects of RED and RIS are profound at elevated temperatures. The long times which are necessary to achieve steady state at high temperatures attest to the extension of the concentration gradient to such depths.

I O N B E A M M O D I F I C A T I O N O F M E T A L S 2 6 5

I 00

d

60

I I I I I 1 1 1 1

A - -

~ I I h [ ; I I t I ~ I0- [0 - z I0 - I I0 0 I01 I0 2 IC ~ 10 4 I0 5 I0 8 10 7

SPUTTERING TIME ( i )

4C

~3o

8

I0

~ , [ , i , ~ , , i ~ , , , i , , f , i ~ , ~ I 0 Cu NI

- , (my) 0 )5 0 . ) 5 v (or) 0 95 0 97

_ B - -

0~ " I 10 2 10 3 10 4

DISTANCE FROM SURFACE (nm)

Fig. 37. (a) Calculated time evolution of the composition in the outermost atom layer of a Ni-40 at% Cu alloy during 3-keV Ni + sputtering at various temperatures. Two sets of initial conditions were used: the thermodynamic equilibrium state of the alloy (solid curves), and the nonequilibrium uniform alloy composition (dotted curves). (b) The corresponding compositional profiles at steady state. The vertical line indicates the boundary between the first and second atomic layers. The migration energies of vacancies and interstitials via Cu and Ni atoms are tabulated. The symbols are used simply to label the curves for different temperatures. (from ref. 80)

Experimental evidence of these observations comes from an experiment

conducted by Rehn et al. [103] in which a Cu-40 at% Ni alloy was bombarded by

5 keV Ar ions at elevated temperatures. AES and room temperature ion

sputtering were used to reveal two different subsurface regions in which nickel

enrichment was observed, both of which decay exponentially with depth. Region

I has a decay length between 20 and 40 nm and region II has a decay length up

to 1600 nm. However, calculated values of the decay lengths were smaller than

the experimental values by factors ranging from approximately 3 to 8.

Nevertheless, the fact that the calculations underestimate the RIS contribution

very deep in the specimen while still predicting a substantial RIS contribution in

the near-surface region suggests that RIS can play an important role in

de te rmin ing nea r - su r face compos i t i ona l changes dur ing sput te r ing at temperatures where defects are mobile.

Shimizu [104], and Shimizu et al. [105-109] as well as others have measured

the surface concentration of Cu-Ni alloys as a function of sputtering time. With

266 G.S. W A S

careful AES and ISS measurements, results have shown the existence of ion

beam induced surface segregation such that the component with lower surface

energy (Cu) tends to segregate to the outermost atomic layer (GA). The result is

enrichment of the atoms of lower surface energy at the surface and, at the same

time, their depletion beneath the outermost atomic layer. This leads to the

conclusion that radiation-induced surface segregation plays as substantial a role

in the preferential sputtering of alloys as kinetic collision processes. Swartzf~iger

et al. [110] confirmed these findings at 200°C and Lam et al. [81] observed

similar results over a range of temperatures, which are consistent with the

picture that an increase in the Cu concentration of the first atomic layer due to

Gibbsian adsorption is balanced by a corresponding decrease in the Cu

concentration in the second layer.

In the Au-Cu system, a similar result is found with preferential sputtering of

Cu atoms producing an enrichment of Au at the the outermost atomic layer and

Au depletion beneath the outermost atomic layer [111-113]. The factors causing

preferential sputtering are differences in both the masses and surface binding

energies of the consti tuent atoms, as well as radiat ion-induced surface

segregation as shown in Fig. 38. In Au-Cu, the mass effect plays a dominant role

to establish the surface composition, followed by the surface segregation of Au

with its lower binding energy, leading to a stable state when equilibrium is

reached. However, surface segregation is considered to be more dominant in Cu-

Ni alloys. Note that the depth scale of these processes is orders of magnitude

shallower than that for RIS.

>

At* 11

b

• A- atom o B- atom

!~ ion enhanced sub-surface i~! redistribution bulk

~: - - i ~ ~ . . t , = o ~

To < TI

Fig. 38. Schematic illustration of the formation of an altered layer on the sample surface under ion bombardment. Solid and dotted curves indicate the composition vs depth profiles for two different temperatures, To and TI. (from ref. 104)


Wicders ich et al. [98] prov ided a nice descr ipt ion of the effects of the d i f ferent

processes on the time evolution of the surface concentration and on the steady state profiles in a Cu-40 at% Ni alloy bombarded by 5 keV Ar ÷ at 400°C, as illustrated in Figs. 39 and 40. The calculations were performed with various

combinat ions of preferential sputtering, d isplacement mixing, radiation- enhanced dif fusion, Gibbsian adsorption and radiation-induced segregation included. Figure 39 shows the time dependence of the Cu concentration at the alloy surface, calculated at 400°C [114]. Note that in the absence of irradiation (curve #1), GA leads to a strong Cu enrichment in the first atom layer. Accounting only for PS and RED during irradiation (#2) causes a monotonic decrease in CCuS to the steady state value, defined by the sputtering probability ratio and the bulk composition. If GA is included (#3), CCu s increases rapidly at

short times owing to radiation-enhanced adsorption, and then decreases slowly to the steady state value. The inclusion of DM reduces the effect of GA (#4). Considering only PS, RED and RIS (#5), CCu s decreases rapidly to the steady state

value due to the sominant effect of segregation. If GA is added (#6) then the effect of RIS is masked. Finally, with the addition of DM (#7), or when all processes are included, CCu s increases initially and then decreases toward the

100

90

8O

3 ~6C

5C cc

4c ar

3C

}, 2c

' I ' I ' r ' I ~ I ' 1 ' I / ~ ' F - - " - 5 -keV Ar ÷ O~ Cu -40 0t % Ni /

- - ~ : 2.5 x I014 ionslcm 2 $ I - - T : 400"C / r ~ iii __

5 /

__ 5 I

I C~ - -2 :PS+ RED

3: PS+ RED + GA ~'--4: P5+ REO + GA * DM

5; P5+ RED + RIS I0 __6 : PS ~" REO + RIS + GA

7: PS ÷ RED + RIS + GA + OM

o__, l , I , I , I l I I I LI , I I IO -4 I0 -3 I0 -2 I0 - I I00 I01 tO Z I03 10 4 II

SPUTTERING TIME (s)

10 ~

Fig. 39. E f f e c t s o f var ious combinations of Gibbsian adsorption (GA), preferential sputtering (PS), radiation-enhanced diffusion (RED), d i sp lacement mix ing (DM), and radiation-induced segregation (RIS) on the time evolution of the surface c o n c e n t r a t i o n o f Cu dur ing sputtering at 400°C. (from ref. 98)

10c o =

c_) b ec g

T ; 400"C . . . . . . . GA (in unbomborded NiCu) . . . . PS + REO ~ P S + RED +GA

~ . . . " - , ~ - - PS + RED +GA+ DM - - " o " - P5 + RED ÷ GA + RIS

• PS + RED +GA+ RIS +DM

0 I I I 0 0 2 I00 I01 102 I03

OISTANCE FROM SURFACE {nm)

Fig. 40. Ef fec t s of var ious combinat ions of the f ive basic processes defined in Fig. 39 on the s t e a d y - s t a t e Cu c o n c e n t r a t i o n profiles during sputtering at 400°C. (from ref. 98)

268 G.S. WAS

steady state value. The effect of different combinations of processes on the

steady-state Cu concentration profile is illustrated in Fig. 40.

I, Implant redistribution during ion implantation

A kinetic model has been developed recently by Lam and Leaf [115] to

describe the effects of these kinetic processes on the spatial redistribution of

implanted atoms during the implantation process. The effects of spatially

nonuniform rates of damage and ion deposition, as well as the movement of the

bombarded surface as a result of sputtering and introduction of foreign atoms

into the system, were taken into account. The evolution of the implant

concentration profile in time and space was calculated for various temperatures,

ion energies, and ion-target combinations for a metal substrate B into which A

atoms are implanted at a flux ~. The local concentrations of vacancies (v), B

interstitials (iB), A interstitials (iA), A-vacancy complexes (vA) and free

substitutional solutes (A) change with implantation time according to a system of

kinetic equations [80] similar to those of eqns. (3.78) through (3.80).

Concurrently with the buildup of solute concentration in the host matrix, the

surface is subjected to displacements both from sputtering and the introduction

of foreign atoms into the system. Sputtering causes a recession of the surface

while implantation causes an expansion. The net surface displacement rate is

controlled by the competition between the rates of ion collection and sputtering.

The temporal and spatial evolution of the surface and subsurface alloy

composition is obtained by solving this set of equations for a semi-infinite

medium, starting from the thermodynamic equilibrium conditions. Sample

calculat ions [115] were performed for low and high-energy Si + and AI +

implantations into Ni, since it is known from earlier studies that in irradiated Ni,

Si segregates in the same direction as the defect fluxes whereas A1 opposes the

defect fluxes [116]. Redistributions of AI and Si solutes in Ni during 50 keV

implantation at 500°C are shown in Figs. 41 and 42, respectively. In the Al-implantation case, CAIS increases with time to a steady state

value of - 50 at%, which is governed by the partial sputtering yield of the

implant. This value is substantially larger than that obtained in very high energy implantation, where sputtering is negligible and CAI s is controlled by RIS.

However, the total implant concentration remaining in the sample is significantly

smaller because of sputtering. Furthermore, the shape of the steady state

implant profile is dictated by PS which controls the boundary condition at the

surface, and by RED and RIS.


2L ............ " t'i ° ,o

: 0 / "" " ~.X 0.8 " / ", I ~ , t . l O . / ' 0.6 A-'°

I 0 4

0 20 40 60 OO o

I" ,Io ,

c~ 0 20 40 60 80

t~Z I t , lO3s

0 20 40 60 80

2t01 , I , ~ 0 20 40 60 80

DEPTH {rim]

Fig. 41. Development of the A1 profiles during 50-keV implantation at 500°C. The normalized damage (Ko) and ion-deposition (PAx) rates are shown in the top portion, and the surface displacements resulting from sputtering are indicated. Note that the concentration scales are multiplied by factors shown in each plot. (from ref. 80)

The evolution of the Si profile is rather different from that of AI, because of

the different RIS behaviors. After a short implantation time, Si enrichment

occurs at the surface because of RIS, and the Si distribution peak starts moving into the sample interior, Fig. 42. With increasing time, CSi s increases

monotonically, attaining a steady state value of -100 at% at t> 2 x 104 s. Unlike

the A1 case, the Si profile shows a significant shift of the implant distribution

into the beyond-range region. This predicted translation of the Si-distribution

peak into the sample interior was consis tent with recent experimental

measurements by Mayer et al. [117] in Si- implanted Ni at e levated t e m p e r a t u r e s .

2 7 0 G . S . W A S

x X

. >.:-" PAx t L'° =~ L / v , , \ -~ 0.6

4 L,, )o, to,. ~F 7' 7 t ~'..i',. ~ 10.2 =

o 0.02 0.04 0.06 o.oe o.,o o

31 ,,.,.6~.

0 ~ . o E 0 0.{ 0.2 0.3 0.4 0.5

i 2 t ,=,,9~ 0 ~ [ ~ I , i , I ,' I [ - -

Z O 0.1 0.2 0.3 0.4 0.5 t.U 2 ~ 8 = 4 6 . 9 i

o 61 ,=,o3s

0 N ~ I , , , 0 O.I 0.2 OJ3 014 01,5

0 L . . . d I ~ I , 1 , I , I

0 0 . 1

I ~ t xlO z

O"-" I

50 l :,t IO z

O J

'°° l ; 50 F III xlO z

O I

,oo~ 5Oo ~ x'lO2

I I 2 3

ATOM LAYER 0.2 0.3 DEPTH (p.m)

0.4 0.5

Fig. 42. Time evolution of the Si profiles during 50-keV implantation at 500°C. The normalized damage and ion deposition rates are shown in the top portion. Surface displacements d resulting from sputtering are indicated. The rapidly- changing Si concentrations in the first three atomic layers are shown in the right inserts (each layer is 0.203 nm thick). (from ref. 80)

4. Microstructural Chan~es

Central to the changes occurring in alloys under irradiation is the alteration of the phase microstructure. This includes radiation-induced precipitate nucleation, precipitate growth and stability, resolution, phase redistribution and changes in phase composition. These processes fall under the category of phase stability. The subject of phase stability under irradiation has been studied for many years and has its origins in the U. S. breeder reactor program. The topic


has been the subject of numerous excellent and recent reviews [57,118-122]

Due to the nature of its origin, the emphasis has been on the reaction of the

microstructure to the deposited energy (typically from neutrons) and less on the

role of the bombarding particle or the change in composition during irradiation.

The commonality with ion bombardment is in the damage introduced during the

irradiation. However, there are a number of additional processes which affect

the microstructure which are more specific to ion implantation, ion beam mixing

or ion beam assisted deposition, such as metastable phase formation, ion- induced grain growth, etc. Consequently, this section is divided into three parts.

Part A briefly summarizes the state of our knowledge in phase stability under

irradiation, part B discusses the formation of metastable phases by ion

implantation or ion beam mixing, and part C describes additional aspects of

microstructural evolution during ion irradiation.

A. Phase stabilitv

The stability of precipitates under irradiation is a consequence of the

processes discusses in section 3. Irradiation affects precipitate stability through

an increased defect concentration, enhanced diffusion, segregation, and ballistic

processes. The increased atomic mobility can enhance the rate of formation or

resolution of a precipitate. The segregation of a solute to a sink can induce local

composit ional changes which are large enough to change the local phase

equilibrium resulting in precipitate nucleation or dissolution. Vacancies and

interstitials may also have a direct effect on nucleation of precipitate phases, by

accommodat ing volume expansion or contraction at the nucleus interface.

Displacement events may cause precipitate shrinkage by physical ly ejecting

(recoil resolution) atoms from the interior to the matrix. The recoil resolution

will be opposed by a diffusive flux from the matrix to the particle and the

balance between these two processes will then determine the degree to which

irradiation will destabilize the precipitate. Irradiation may also disorder regions

in a thermodynamically stable ordered precipitate giving rise to their dissolution

by virtue of an increased solubil i ty of the disordered region. Finally,

precipitates may be nucleated under irradiation. The following discussion begins

with a treatment of radiation-induced nucleation of precipitates.

(i) Precioitate nucl¢ali0n, Katz and Wiedersich [123] developed an expression

for the nucleation rate of precipitate nuclei at steady state which was directly

272 G.S. WAS

proportional to the arrival rate, [3e of solute in the saturated solution and, hence

to the radiation-enhanced diffusion coefficient,

j = [3ef(1)/rle(1){l~[s(x)rle(x)(C/Ce)X]-I }-1, (4.1)

where f(x) is the concentration of embryos containing x atoms per unit area,

lle(X) is the equilibrium concentration of embryos in the saturated solid solution,

s(x) is the surface area of an embryo of x atoms, and C/Ce is the ratio of solute

concentrations in the supersaturated and saturated solid solution. Note that at

steady state, J is independent of both x and t.

Mruzik and Russell [124] developed a formulation for the nucleation rate

applicable to calculation of the rate of incoherent precipitate nucleation in

irradiated metals. The nulcei are taken as spherical and of elemental

composition. Each particle is characterized by the number of atoms it contains, x,

and by the number of excess vacancies it contains, n. Processes giving rise to

changes in the state of the particle are those involved in growth plus the

possibility of a nucleus being struck by a displacement cascade and dispersed

into single solute atoms, vacancies, and interstitials. The calculation focuses on

the number of nuclei growing past a certain value of x, per unit of volume and

time. At steady state, this nucleation flux is independent of x and is given by

Js(x) = I2 [13xp(n,x) - Ctx(n,x)p(n,x+l)], (4.2)

where ~x is the arrival rate of solute to the embryo, Ctx is the loss rate of solute

from the embryo, and p(n,x) is the number of particles of n excess vacancies and

x solute atoms, per unit volume of material. The 13's are determined by the

concentrations and mobilities of the respective point defects and the time rate of

change of p(n,x) is obtained from a balance between particles entering and

leaving a given (n,x) size class.

Supersaturated vacancies were found to have a profound effect on

enhancing precipitate nucleation. Furthermore, no reasonable values of solute

supersaturation and interfacial energy will give an observable rate of nucleation

in the absence of a vacancy supersaturation. While the presence of excess

interstitials reduces the nucleation rate somewhat, the rate is still considerably

higher than without vacancies. Frost and Russell [121] also showed that

i r r a d i a t i o n - i n d u c e d vacanc ies s tabi l ize par t ic les for supe r sa tu ra t ed ,

undersaturated or saturated solutions.

Whereas the increased nucleation rate resulting from the radiation-enhanced

diffusion should be a general phenomenon, other effects of radiation on


nucleation have been suggested. For example, misfit strains can be reduced by

incorporation of excess point defects of the proper type into nuclei [125], as a

consequence the equilibrium concentration, ~e(X), of nuclei would increase and

with it the nucleation rate. Cauvin and Martin [126] also suggested that

enhanced vacancy-interst i t ial recombination at solute clusters may stabilize

nuclei if solute segregation is associated with the defect flux to the clusters.

A very important and practical way in which precipitation can occur under

irradiation is as a result of radiation-induced segregation [127]. As discussed in

section 3.E, significant fractions of randomly produced defects annihilate at

sinks, thus inducing defect fluxes. A preferential association or exchange of

specific alloy components with defects couples net fluxes of alloy components to

defect fluxes, which in turn alters the local composit ion near defect sinks.

Usually, the matrix near sinks becomes depleted of the large atomic size

components and enriched in the small atomic size components of the alloy. Local

enrichments of solutes may be sufficiently large to exceed the solubility limit

and precipitation can then occur in nominally solid solution alloys. Precipitation

will continue until the matrix concentration decreases to a level that permits a

sufficiently steep solute gradient to balance the defect flow-induced solute flux

to the sinks by solute back diffusion. The temperature range in which radiation-

induced precipitation is predicted to occur also goes through a maximum as a

function of binding energy. The temperature range of precipitation shifts to

lower temperatures with lower displacement rates, Fig. 43. A prime example is

the precipitation of Ni3Si on surfaces, dislocation loops and on grain boundaries

of a dilute Ni-Si alloy [129].

The precipitation of ordered 1" (Ni3Si) has also been reported in type 316

stainless steel after neutron irradiation below ~525°C [130,131]. This phase is

not observed in 316 SS without irradiation and dissolves during prolonged post-

irradiation annealing [130,132]. The ~' phase is most likely a consequence of the

strong segregation of Si and Ni to defect sinks. Sethi and Okamoto [133] have

measured appreciable enrichment of Si and Ni and depletion of Cr in the near

surface region of ion-irradiated austenitic Fe-Cr-Ni-Si alloys. Neutron

irradiations also induce precipitates of a ternary nickel silicide [130,131,134], G-

phase and a silicon rich M6C [134]. Radiation-induced G-phase but not "t' has

been observed in ion irradiated type 316 stainless steel with Si and Ti

modifications [135]. However, both phases are induced by Ni-ion bombardment

in austenitic Fe-12 wt% Cr-15 wt% Ni alloys with Si, Mn and Ti additions [57].

High energy Cr+ irradiation at 550°C of a ferritic steel containing V, Mo or Si

produce the M23C6 phase. Evidence exists to suggest that the incorporation of

Mo and V into the M23C6 before irradiation may be a necessary prerequisite for

274 G.S. WAS

measurable stability of this phase. In this alloy, all the grain boundary phases which precipitate upon heavy-ion irradiation are chromium-rich despite being

formed at an interface where chromium depletion is occurring, suggesting that in

this case the kinetics of precipitate formation are the dominant effect.

20O

160

120

8C--

4C

0

i I i t i i i

C ° = 10 -3 , H~tQ= ;~.0 eV, H~t s = 0 . 0 5 eV

NO PRECIPITATION

~ t ~ K o = I0 - 3

/ Ko=,o 6 -.~ / ' / t

t

I

x ' i . . - ~ L 4 0 0 600 800 lOOt)

T ( = C )

Fig. 43. Effect of defect-production rate on the temperature dependence of solute enrichment at a foil surface (no precipitation) and at the precipitate- matrix interface (with precipitation). The parameters are chosen for nickel. (from ref. 128)

(ii) Precipitate erowth and ~tability The earliest analysis of precipitate stability

under irradiation was conducted by Nelson, Hudson and Mazey [136] who

considered the balance between precipitate shrinkage due to irradiation

resolution or disordering, and reprecipitation speeded by irradiation-enhanced

diffusion. Particles are predicted to approach an equilibrium radius from larger

or smaller size, at which point the rate of reprecipitation from the enriched

matrix just balances the rate of solute loss from the particle due to disorder

dissolution. This size dependence of particle stability is reversed from the usual,

with smaller particles being more stable than larger particles. This is because

dissolved material could also re-precipitate, at a rate governed by the

irradiation-enhanced diffusion coefficient. The rate of mass loss of a particle of

radius r due to disordering was found to vary as r 2, and the rate of re-


precipitation to vary as r. Thus, big particles were predicted to shrink and small

particles to grow to a certain 'equilibrium' size as shown by the solid curve in

Fig. 44. The model predicted that particles should approach the stable particle

size after modest doses of a few dpa. The stable particle size was predicted to

increase and the matrix solute concentration to decrease with increasing

t e m p e r a t u r e .

dr at

Nelson, Hudson, ond Mazey _ . Schwortz P, Ardell

/

/Unstoble/\ i / / " N o Solution

/ /

Fig. 44. Calculated growth rate for ordered, coherent particles undergoing

irradiation-induced disorder dissolution. (from ref. 137)

Nelson did not, however, consider the increase in solubility which comes with

a decrease in particle size and makes the smaller particles less stable. Russell

[137] reported that Ardell and Schwartz accounted for the effect of curvature-

enhanced solubility, with the results shown in Fig. 44. In some cases there is no

'equilibrium' size. Disorder-dissolution can reduce the particles to such a size

that equilibrium solubility is high enough to put all particles back into solution.

Thus, by dissolving the equilibrium phase, irradiation will have forced the

system into such a state that a non-equilibrium phase could precipitate out.

Subsequent analyses of this model [138-141] produce significantly different

results including disagreements as to whether a unique steady state size distribution should be expected.

A theory for the stability of precipitates under irradiation was developed by

Maydet and Russel l [125]. They developed analytical expressions for the

locations of nodal lines in (n,x) space where the net rate of solute capture (~) or

of vacancy capture (h) is zero and for the critical point at which these lines

276 G.S. WAS

intersect, Fig. 45 They found that a critical point exists only if A¢ < 0, where A~is

an irradiation modified free energy which determines phase stability under

i r radiat ion,

At) = -kTlnSx [Sv(1-~i/~v)] 8 - kT[lnSv(1-13i/13v)]2/4B, (4.3)

where fi = (f~-f2m)/f2m, (4.4)

and B = f~E/9kT(1-v), (4.5)

and where Sx is the ratio of actual and saturation concentrations of solute, Sv is

the ratio of actual and saturation concentrations of vacancies, f2 is the atomic

volume of the precipitate and ~m is the atomic volume of the matrix, E is

Young's modulus and v is Poisson's ratio. In that usually ~i/~v < 1, irradiation

will tend to enhance the stability of a phase for which 5 > 0, and destabilize in

the reverse case. The former is usually the case since matrix solid solutions tend

to be more closely packed than are precipitate phases.

"J,-o

\CRITICAL POINT

Fig. 45. Results of critical point/nodal line analysis of incoherent particle

behavior under irradiation. (from ref. 137)

For an undersize precipitate phase (5 < 0) to grow from a slightly

supersaturated solid solution without prohibitive strain energy, the particle

must emit vacancies into the matrix. In the absence of excess vacancies this is

easily done, as vacancies arrive at and leave the interface at the same rate (in

the absence of growth or decay), and there is no trouble in establishing a net

flux out to allow growth.


Under irradiat ion, the vacancy emission rate is not altered, but the arrival

rate is increased by several orders of magnitude. It is then almost impossible to

achieve a net emission of vacancies. There will instead tend to be a net gain of

vacancies, resulting in a strain energy which is easiest relieved by emission of

solute atoms in the face of the slight solute supersaturation. The excess

vacancies thus destabilize the undersized precipitate phase. The same

arguments may be used to understand stabilization of an oversized precipitate.

Cauvin and Martin [142] reanalyzed Russell 's model for the growth of

incoherent precipitates and showed that indeed, it qualitatively accounts for

precipitation in the case of undersized precipitate atomic volume. More

importantly, they observed that under appropriate conditions, undersaturated

AI-Zn solid solutions give rise to a homogeneous precipitation of clusters which

they argue to be Guiner-Preston zones of incoherent Zn precipitates, the atomic

volume of which is smaller than that of the matrix.

They conducted a systematic TEM study of 1 MeV electron irradiation damage

in A1 1.9 at% Zn solid solution over a wide range of irradiation fluxes and

temperatures, and showed that Zn precipitates form under irradiation at

temperatures well above the Zn solvus temperature outside irradiation. This

upward shift of the Zn solvus temperature under irradiation is dose rate

dependent, thus defining a temperature dependent dose rate threshold for the

occurrence of Zn precipitation in A1Zn undersaturated solid solutions. The

authors [142] suggest that an attractive solute-defect interaction in conjunction

with defect-induced solute fluxes in the same direction as that of the defects,

stabilize solute clusters present as a consequence of concentration fluctuations.

Because of the defect-solute attraction, the defect concentration in solute rich

clusters is enhanced. This leads to higher recombination losses within the

clusters, which thus act as defect sinks. The clusters then grow by radiation-

induced segregation.

The discovery of irradiation-induced precipitation in undersaturated solid

solutions discredited the simple picture of the effects of irradiation on phase

stability which described the phenomenon as simply resulting from a balance

between radia t ion- induced disordering and radia t ion-accelera ted diffusion

towards the equilibrium state. Indeed it was learned that the solubility limit is

dose rate dependent. Irradiation-induced precipitation is a result of radiation-

produced point defects, and it is the supersaturation of these defects which

provides the driving force for precipitation. For a given irradiation temperature

and dose rate, the point defect supersaturation in the solid solution under

irradiation is a function of the solute content and of the point defect sinks and

trap density. Once precipitates are formed, they act as traps or sinks for point

278 G.S. WAS

defects. The point defect supersaturation in the matrix is therefore lowered by

the presence of the precipitates; precipitation will cease before the solute

content of the matrix has reached the solubility limit without precipitates.

(iii) Coarsening. The theory for thermal coarsening was developed by Lifschitz

and Slyozov [143], and Wagner [144]. Here, particles with a diameter larger than

the mean diameter grow under the driving force of the interfacial free energy at

the expense of particles smaller than the mean diameter. During coarsening, the

precipitate size distribution and volume fraction remain essentially unchanged

while the mean size increases such that r 3 -ro 3 = Kt where K a D, the diffusion

coefficient. Precipitate coarsening under irradiation has been studied by a

number of authors [138-141]. The main effect of irradiation is the acceleration

of the rate of particle growth due to radiation-enhanced diffusion. This has been

confirmed for Ni-12.8 at% A11145,146] and Ni-12.7 at% Si [147,148] as will be

discussed in section 4.A.vi.

Baron et al. [139] considered the effects of irradiation resolution and

enhanced diffusion, and allowed the matrix concentration to rise above the

thermal value. Particles were allowed to change size by two processes: (1)

steady drift due to the rates of thermal and irradiation resolution being greater

(or less) than the rate of reprecipitation from the matrix, and (2) random walk

due to statistical fluctuations in the rates of solute addition and loss. For

particles which are initially larger than the maximum stable size, particle

shrinkage r varies linearly with time, with the proport ionali ty constant

depending only on the irradiation parameters. However, for initial particle sizes

much smaller than the stable size, the coarsening has an r 3 versus t dependence

that is very similar to that for thermal coarsening and the proportionality

coefficient in both cases involves the diffusion coefficient.

Urban and Martin[149] developed a theory for precipitate coarsening that

includes point defect recombination at precipitate interfaces as an additional

driving force. When a defect of opposite type as those already trapped arrives

at the particle, it annihilates immediately so that three types of precipitates

coexist: those with trapped vacancies, those with trapped interstitials and those

without trapped defects. Because of the irreversibJlity of recombination, net

fluxes of defects to the precipitate matrix interfaces are set up which affect the

coarsening kinetics if radiation-induced segregation occurs. They have shown

that for a system such as a dilute A1-Zn alloy, in which vacancies are trapped

preferentially at the interface and in which the Zn solute segregates in the same

direction as the defect fluxes, the coarsening kinetics is accelerated and the size


distribution widened initially during irradiation, but both approach their purely

radiation-enhanced coarsening values at long times.

(iv) Precioitation of imolanted gases. Another example of precipitate stability

due to implantation was discovered in 1984 when heavy inert gases (Ar and Xe)

were implanted into aluminum and precipitated in a solid form [150,151].

Electron diffraction studies show identical symmetry of the rare gas diffraction

pattern and of the host metal diffraction pattern indicating epitaxial alignment

of rare gas crystallites and host matrix. For the lighter rare gas Ne, the

occurrence of liquid Ne precipitates under high pressures in implanted metals at

room temperature has been reported [150,152]. For the lightest rate gas He,

evidence for solid He in small cavities at room temperature has been obtained

for implanted Ni [153]. These results demonstrated that inert gas bubbles in

metals formed by implantation at ambient temperatures are under high

pressures, of the order of several GPa.

Recently, Birtchaer and J~iger [154] performed a careful study of the

microstructural changes and the precipitation of Kr in thin films of AI during 65

keV Kr ÷ implantation at room temperature. Their TEM observations show that

Kr becomes trapped in a dense population of growing cavities. At low fluences (<

1015 Kr+/cm 2) dislocation loops and the formation of a dislocation network is

observed. The loops increase in size as the Kr fluence is increased until (2 x 1014

cm-2) their interaction results in the formation of a dislocation network. At high

fluences (> 1015 cm-2 the microstructure is dominated by a high concentration of

cavities with larger cavities on the grain boundaries. At a fluence of 1.3 x 1016

cm -2, the single crystal AI grains contain a high density (1 x 1020 cm-3) of

cavities whose average diameter is 1.7 nm with sizes up to 2.7 nm. Increasing

the Kr fluence to 2.2 x 1016 cm -2 results in an increase of the average cavity

diameter to 2.8 nm with a maximum diameter of 5 nm, and a decrease of the

cavity density to 0.5 x 1020 cm -3. At a fluence of 5.5xi016 cm -2, the size

distribution contains cavities as large as 40 nm. In all cases, grain boundary

cavities were much larger than the largest cavities within the grains [155]. The

authors suggest that the formation of visible cavities containing the implanted Kr

can occur by the growth of Kr-vacancy complexes due to Kr absorption. Kr

transport to cavities could result from diffusion by vacancy or divacancy mechanisms.

Evans [156] notes, however, that there appears to be general agreement that

the result can only be consistent with a pressure-driven cavity growth process

such as loop punching [157] in which a cavity can gain vacancies at the expense

280 G.S. WAS

of punching out interstitial loops into the matrix. This view is supported by a

recent compilation of results for krypton and xenon in a number of metals which

showed that the pressure of the solid inert-gas precipitates was a strong

function of the metal shear modulus [158].

(v) Order-disorder transformations. The effect of irradiation on ordered alloy

phases can be described as a balance between two conflicting processes: the

disordering produced by the atomic displacements during defect production and

the ordering facilitated by the thermal migration of excess vacancies and

interstitials [159-161]. The rate of change of the order parameter, S, is the sum

of the irradiation disordering and radiation-enhanced thermal ordering rates:

dS/dt = (dS/dt)irr + (dS/dt)th. (4.6)

The disordering rate depends on the rate of atom replacement, which should be

linear with the irradiation flux. If the atoms are replaced randomly by other

atoms, we find that the disordering rate is proportional to the order parameter:

(dS/dt)irr = eKS, (4.7)

where E is the disordering efficiency, which depends on the type of radiation.

Note that this approximation shows no dependency on temperature.

The ordering rate is proportional to the concentration of mobile defects, the

rate at which they jump, and the fraction by which ordering jumps exceed

disordering jumps. The ordering rate therefore depends on the radiation flux

through the dependence on defect concentration. It depends on temperature

through the defect concentration and the jump rate and jump preference terms.

As the temperature is lowered, the fraction of ordering jumps should increase

because of an increasingly favorable Arrhenius factor. Therefore, in the regime

where diffusion to fixed sinks dominates, the ordering rate should increase as

the temperature is lowered. Only when the temperature is reached at which

direct recombination of defects becomes important will the trend reverse.

However, at temperatures where vacancies are immobile, even the enhanced

ordering rate is insignificant and the disordering process will dominate. At

higher temperatures where the thermal equilibrium vacancy concentration is

large, there is little enhancement of the thermal ordering rate by irradiation. As

a function of dose, the steady-state ordered and disordered states shift to lower

temperature with lower dose rates.


Experimental evidence is in good agreement with theory in many cases. For

example, Banerjee et al. [162] have shown that the long-range order in Ni4M o

remains at the equilibrium order parameter above 520K during irradiation at 5

x 10 -3 dpa/s. Below that temperature, the steady state long-range order

decreases rapidly with irradiation temperatures becoming essentially zero below

450K. The decrease in order at low temperatures is exponential with dose.

More examples of irradiation disordering are provided in section 4.B.i.

(vi) Phase redistribution and composition modifications, Phase redistribution

has been frequently reported, but only a few systematic investigations exist.

The most extensive studies have been reported by Potter and coworkers in a Ni- 12.8 at% AI alloy [145,146] and in a Ni-12.7 at% Si alloy [147,148]. Both alloys

are two-phase in the temperature range of the Ni-ion bombardment investigated

(400-700°C). Solution annealed and quenched samples of Ni-12.8 at% A1 were irradiated with Ni ions at intermediate temperatures. Irradiation at low doses

[153] causes the formation of a uniform distribution of small 3" precipitates

except near interstitial dislocation loops and other sinks, Fig. 46. As the

dislocation loops grow with increasing dose, the precipitate-free zones (PFZ)

enclosing the loops grow correspondingly by dissolution of the precipitates

because of radiation-induced segregation of Ni into these regions. The precipitates in the sink-free regions between PFZs coarsen at a radiation-

enhanced rate. At higher doses (> 15 dpa at 550°C), ~'-precipitates renucleate

within the PFZ colonies. Apparently the continued drain of Ni toward the loop

perimeter reverses the initial Ni-enrichment in regions of the zones that become

remote from the dislocations, and ultimately reprecipitation of Ni3AI occurs

there. A consequence of the reprecipitation process is a decrease in the average

precipitate size during prolonged irradiation.

While radiation-induced segregation in two-phase Ni-A1 alloys promotes the

single phase "t solid solution in regions near sinks, the opposite occurs in two-

phase Ni-Si alloys [147,148], Fig. 47. In this case, low doses causes the formation

of small ~,' (Ni3Si) precipitates in the initially solution-quenched alloy. At higher

dose, disk-like precipitates grow in thickness and diameter with the growing

dislocation loops, consuming nearly all the "t' in the matrix. At grain boundaries

and at surfaces, continuous Ni3Si films grow during irradiation at the expense of

the precipitates in the interior of grains [148,163].

282 GIS. WAS

/

\

SUOSIjR f ~Ct ', NT{ B i; i~

Fig. 46. Formation of y'-Ni3Al away from defect sinks in a solid solution Ni-AI alloy because of RIS. The dark field micrographs from a two-phase Ni-AI alloy show (a) y' particles concentrated near the center of a thin foil and (b) preferential formation of y' particles away from interstitial loops during ion bombardment. (from ref. 62)

" 1

1~-. . , -~ ~ , .' 'G ] w - 4

, t, ! .... 4 _ ~ L " ,,:

Fig. 47. Formation of y'-Ni3Si on defect sinks in a solid solution Ni-Si alloy because of RIS. The dark-field micrographs show (a) the anti-phase domain structure in a contiguous surface coating: (b) toroidal Y' precipitates on interstitial loops: and (c) a grain boundary coated with y'. (from ref. 62)


In addition to changes in the phase distributions of an alloy under irradiation,

significant changes can occur in the composition of the phases. Wiedersich [118]

provides an explanation for such an occurrence. At thermal equilibrium, the

compositions on both sides of the interface between matrix and a second phase

precipitate are uniquely defined. As long as equilibration can quickly occur

across the interface, this region will adjust so that adjacent matrix precipitate

compositions correspond to those of the equilibrium phase diagram. Thus,

excess solute carried by defect fluxes from the matrix to a precipitate interface

is accommodated by growth of the precipitate at a composition determined by

the phase diagram. In binary alloys, this composit ion is a function of

temperature alone and, to the degree that the composi t ion within the

precipitates can be considered spatially constant, the precipitates are the

equilibrium phase.

In multicomponent alloys, the compositions of second phase precipitates can

be altered significantly from those present in the alloy at thermal equilibrium

by radiation-induced segregation. An example is the increased Ni and Si

concentrations and the decreased Cr concentration at defect sinks by radiation-

induced segregation in austenitic alloys [133,134]. If persistent defect fluxes

from the matrix to second phase precipitate interfaces are maintained during

irradiation, the precipitates will become enriched in Ni and Si and depleted in Cr.

Thus, Wiedersich points out [118] that the additional degrees of freedom in

multicomponent alloys permit, even in the absence of concentration gradients

within the precipi tates , the composi t ions of second phases to become

significantly different during irradiation from those in the unirradiated alloy.

Williams, Boothby and Titchmarsh [134] conducted a study of four 12Cr-15Ni

austenitic alloys containing silicon in the range 0.14 to 1.42 wt% that were

irradiated with neutrons to a dose of approximately 20 dpa at temperatures in

the range 400°C to 645°C. After irradiation, only the low silicon alloy remained

predominantly austenitic. At high temperatures the transformation to ferrite

was confined to the grain boundary whereas at lower temperatures the

transformation often extended throughout the grain. Nickel and silicon

segregate to, and chromium and iron are depleted at grain boundaries. In

addition, intragranular regions separate into nickel and silicon rich, chromium

and iron depleted, and chromium and iron rich, nickel and silicon depleted zones,

Fig. 48. At the highest irradiation temperatures, the silicon remains in solution

in silicon rich intragranular regions, and chromium rich, nickel depleted regions remain austenitic. The scale of the compositional variations is on the order of

700 nm. However, at lower temperatures silicon rich precipitates are formed

284 G.S. WAS

within the silicon rich regions and the chromium rich regions transform toferrite.

The wavelength of the compositional oscillation is considerably shorter, on the order of 25-50 nm, Fig. 49.

s°i • 70 =- . . . . .

+o

2C/ Cr i

+ i

0 I i . . ~ - - d + I , _ ,

ill p s+ , , / ~ , _

1,5 1,0 0,5 0 0,5 1,0 1,5 Distance from Grain Boundary (~m)

Fig. 48. Compositional variation near a grain boundary in a 12Cr-15Ni alloy containing 0.95% Si after irradiation to 23.6 dpa in EBR II at 645°C. (from ref. 134)

~1 ,0

.~o,5

E 8

400

• Measured values i D Values inferred from r n i c r o s ~ r u c l u r y

/ a ~

500 600 Irradiation Temperature (°C)

700

Fig. 49. Variation in the scale of compositional fluctuation with irradiation temperature in the alloy in Fig. 48, irradiated in EBR II. (from ref. 134)


These transformations are a consequence of extensive irradiation-induced

solute redistribution. However, the authors argue[134] that the intragranular

solute redistribution does not appear to be associated with point defect sinks,

but that segregation may have originally occurred at sinks such as dislocation

loops which subsequently grew away or that irradiation-enhanced spinodal

decomposition is responsible.

M u r p h y [164] recently addressed these results based on calculations he

performed using the 'random-alloy model' for diffusion in concentrated alloys

developed by Manning [165]. His intent was to investigate whether an

irradiat ion-induced instabili ty can produce composi t ional f luctuations in a

concentrated alloy that is thermodynamically stable. He determined that

spinodal decomposi t ion was unlikely in thermodynamical ly stable alloys.

Instead he sugges ted two al ternat ive explanat ions for the observed

compositional instabilities.

It is generally thought that silicon atoms interact strongly with irradiation-

produced vacancies and interst i t ia ls [166]. These i r radia t ion- induced

instabilities caused by dilute concentrations of elements such as silicon produce

spatial fluctuations in the concentrations of vacancies and interstitials which in

turn can cause fluctuations in the concentrations of the major alloying

components. Thus, it is possible that the oscillations in composition in Fe-Cr-Ni

alloys arise because of the presence of solute atoms which act as point-defect traps.

An alternative explanation is in the underlying sink structure. Calculation of

the wavelengths obtained when only the instabilities in the vacancy-loop

population are included [167] show good agreement with the wavelengths of

compositional fluctuations observed by Williams et al. [134] at low temperatures.

Spatial fluctuations in the density of network dislocations or other point-defect

sinks may be able to explain the development of compositional fluctuations at higher temperatures.

A general trend for most of the secondary phases in austenitic and high-

nickel fcc alloys is that irradiation frequently increases the Ni and Si content of

thermally exist ing phases, and radiat ion-induced phases form with high

concentrations of these elements [130,132,134,135]. These observations lend

strong support for the contention that radiation-induced segregation plays a

major role in the development of the phase-microstructure in these alloys.

286

B. Metastabl~ ohases

G.S. WAS

Ion implantation and ion beam mixing are effective methods of forming

nonequilibrium or metastable phases in alloys. With this technique, metastable

alloys which were previously inaccessible can be readily produced and

examined. Since the term "metastable" implies a phase with a free energy

higher than that of the stable phase under the prevailing conditions of

temperature and pressure, it is natural to look to thermodynamics for an

explanation. Experimental results seem to indicate a strong role of

thermodynamics in the tendency to form metastable phases. Intermetallic

compounds with small ranges of solubility and complex crystal structures are

prime candidates for transformation to a metastable phase [168]. Also, the

change in the free energy of the solid due to the ion induced defect buildup

argues for a thermodynamic explanation [169]. However, not all transformations

can be explained on a purely thermodynamic basis.

Hung and Mayer [170] provided a concise summary of the role of kinetics in

metastable phase formation. They state that at low temperatures, ion mixing is

similar to a quench process where the atom configurations are essentially

determined during the relaxation period following the collision events. Because

kinetics are restricted, the formation of complex crystalline structures is unlikely

and ion mixing will usually result in solid solution, simple cubic structures or

amorphous structures. The structure of the metastable system is, however,

influenced by the equilibrium nature of the system. Those systems with many

intermetallics will tend to form amorphous phases while those with no

intermetallic alloys show a tendency to form solid solutions in mixing. At high

temperature, atom mobility is significant and equilibrium phases will usually

form.

Metastable phases can be formed by ion irradiation, ion implantation and ion

beam mixing. Differences in the transformation process between these three

techniques can provide insight into the mechanism. For example, in ion

irradiation experiments, the main purpose of the radiation is to impart damage

to the lattice. However, in ion implantation, the implanted species provides a

chemical alteration to the target as well. Ion beam mixing experiments are

designed to follow the transformation by rapidly altering the bulk content of the

film. Metastable phases formed by irradiation usually occur by one of four

types of transformations [171]:


o r d e r <--> d i so rde r

crystal structure A --> crystal structure B

crystal structure A <--> a m o r p h o u s

crystal structure A --> quas ic rys ta l l ine

Each of these transformations will be reviewed individually, followed by a

d iscuss ion of the the rmodynamic and kinetic factors control l ing the

t r ans format ions .

(i) Qrder <--> disorder transformations. Order - disorder transformations can

occur in either direction under irradiation, depending upon the composition and

structure of the system and the target temperature under irradiation. Schulson

[159] and Wilkes et al. [160,161] extensively reviewed the subject of the effects

of irradiation on ordering of alloys in the late '70s and early '80s. But the most

detailed model of the phenomenon was developed by Banerjee and Urban[162]

in which radiation-enhanced ordering is assumed to occur by the thermal motion

of vacancies only. The model treats the ordering by vacancy-atom exchange

between the sublattices with the activation energy and, therefore, the jump

frequency, depending both on the degree of the existing order and on the type of

jump. The steady state vacancy concentrations are calculated according to a

modif icat ion of reaction rate theory [172,173], taking into account the

differences in concentrations on the sublattices that can develop in ordered

alloys.

At lower temperatures where vacancies are immobile, ion irradiation of

ordered alloys often leads to radiation-induced disordering as discussed in

section 4.A.v. This occurs very quickly in some systems. For example, the '~'

phase (L12), Ni3AI, is extremely unstable under irradiation [174], becoming

disordered at a dose of 2 x 1014 i/cm 2 [175]. On the other hand, Fe3AI (bcc) and

FeAI (bcc-B2) undergo only partial disordering after 40 dpa of 2.5 MeV Ni +

irradiation [168]. Hence, factors besides dose play a role in the order-disorder transformation reaction in alloys.

Many compounds undergo chemical disordering prior to amorphization under

electron irradiation. Luzzi and Meshii [176] showed that of 32 compounds

irradiated, all underwent chemical disordering and 15 amorphized. They

concluded that irradiation-induced chemical disordering provided the driving

force for amorphization, and cited the difficulty in forming the amorphous

structure in pure metals as support for this argument. Until recently [177],

there were no observations of chemical disordering prior to amorphization

288 G.S. WAS

during ion irradiation, giving rise to speculation that disordering is not necessary

because of the much higher density of damage in ion-induced cascades as

compared with electron irradiation. However, as will be shown in section 4.B.iv,

disordering prior to amorphization is observed in Zr3A1 and FeTi, but not in NiAI

which also did not amorphize [177].

~ii) Crystal structure A --> cry~tal structure B t ransformat ions , Numerous

examples exist on the transformation from one crystal structure to another upon

ion irradiation. One of the best documented examples is the transformation of a

pure metal, nickel, from fcc to hcp under irradiation. This transformation has

been found to occur during irradiation with a variety of species including

neutrons, chemically inert elements such as He and Ar, the metalloids P and As

as well as self-irradiation [178]. Observations on P-implanted high purity Ni

[179] gave an orientational relationship between the new phase and the fcc

matrix similar to that observed for martensitic fcc-->hcp transformations. The

transformation in Ni is thus believed to be martensitic. TEM examination of Sb-

implanted Ni shows hcp particles extending to depths 20nm beyond the

implanted depth, but dechanneling is present up to 130nm. This suggests that

the defect distribution is playing a role in the structure transformation.

Ion irradiation has also been found to induce phase transformations between

bcc and fcc phases in iron-based austenitic alloys [180]. The most prominent

example is the fcc to bcc transformation of 304 stainless steel following

implantation with 3 x 1016 Fe/cm 2 at 160 keV. Although this dose amounted to

an increase in the Fe alloy composition by only 1 at% (67 at% Fe nominal), the

structure transformed from fcc to bcc. The orientation relationship was neither

the Kurdjumov-Sachs nor the Nishijima-Wasserman relationships typically found

in ion-irradiated steels [180], but instead obeyed the following relationship:

(100)bcc II (100)fcc and [010]bcc II [011]fcc.

Follstaedt [181] suggested that the transformation need not be occurring

martensi t ical ly , but that the increased defect concentrat ion and hence,

diffusivity, may be responsible for the transformation.

It should also be noted that this transformation is inherently different from

that of nickel under irradiation. In the present case, the transformation is from

the metastable state to the equilibrium structure, whereas in the case of Ni, the

transformation is from the equilibrium fcc structure to a metastable hcp

structure. Some insight may be gained into the driving force for this type of


transformation through the experiments of Eridon, Was and Rehn [183]. In these

experiments, a target consisting of alternating layers of Ni and AI in the atom

ratio 3:1 was irradiated with 0.5 MeV Kr ÷ ions at 80 and 300K. Mixing to 1 x 1016 Kr/cm 2 produced a dual phase structure consisting of disordered 1,' and a

metastable hexagonal ideally close-packed phase with the same interatomic

distance as the disordered "y' phase. Thermodynamic modeling of the hcp and

disordered "y' (fcc) phases showed that the heats of transformation, AHs-ms for

the two metastable structures were within -1% of each other, indicating the lack

of a preferred metastable structure, hence the observation of the dual-phase

s t ruc ture . Several additional examples of crystal structure transformation exist, such as

the transformation of the FeV-~ phase to a fine-grained, bcc-B2 type structure

[168]. Hung et al. [170,184,185] showed that A13Ni2 (hP5) bombarded with 0.5 MeV Xe + to 2 x 1015 cm -2 transformed into the amorphous phase plus AINi (bcc).

The structural transformations in the Ni-AI system are summarized in Figs. 50

and 51. Similarly, irradiation of Pd2AI3 (hPs) with 0.5 MeV Xe ions to a dose of 2

x 1014/cm2 caused decomposition to the PdAI (bcc) and an amorphous phase

[170]. These data indicate that the transformation from one crystal structure to

another is readily obtained during ion implantation.

Lil ienfield et al. [186] provided an explanation for understanding the

transformation of the trigonal (D513) structure (e.g., Ni2AI3, P d 2 A I 3 ) t o the

bcc(B2) structure (NiAI, PdAI). The Ni2A13 structure can be viewed as being

made up of pseudo NiAI cubes, every other one having a vacant Ni body center

site. To construct the Ni2A13 structure from the NiAI structure simply requires

that every third plane of the Ni atoms perpendicular to the NiA1 [111] direction

be replaced by vacancies. This vacancy ordering results in a contraction of the

axis parallel to the NiAI [111] direction, which reduces the crystal symmetry

from cubic to trigonal.

Since the unit cells of Pd2AI3 and Ni2AI 3 each have 5 atoms and the unit cells

of PdAI and NiAI each have 2 atoms, Lilienfield [186] raises the question of

whether stability under ion irradiation depends on the complexity and size of

the unit cell. Since atomic species have limited mobil i ty under room

temperature irradiation, it is plausible that only simple structures with small

unit cells can reorder. This question will be dealt with in more detail in section

4.B.iv on current theories of amorphous phase formation.

Lilienfield et a1.[186,187] also produced a metastable phase in the A1Zr

system by room temperature ion mixing alternating layers of A1 and Zr in the composit ion AI80Zr20 to form an amorphous structure. The samples were then

subjected to either thermal anneals or ion assisted thermal anneals to form the

290 G.S. WAS

metastable phase. This same phase was also formed directly by ion mixing

co d epos i t ed , amorphous AI80Zr20 or the multi layered film at elevated

temperature. The latter showed that it was possible to form the metastable

phase directly by mixing without benefit of a preformed amorphous phase. The

resulting phase is an ordered cubic metastable phase that has the same structure

as AuCu3, which is an fcc structure with Au in the corners and Cu in the faces.

500

t80C

o ,50c

g ix

fO00

bJ )--

500 50 ioo

ATOMIC PER CENT Ni Ni

o B n n e o l : 3 5 0 C ~ N i A I 3 , NizAI3, NiAI, Ni3AI

Imp lon t : 5 0 0 k e V Xe [ 'N iAI3 - omorphous 2xlOIS/cm z ~NizAI 3 - NiAI

~NJAI - N iAI ~Ni3AI -, disordered

Fig. 50. Sample con f igu ra t i on , equilibrium phase diagram of Ni-A1 and results of multilayered samples preannealed at 350°C fol lowed by irradiation with 0.5 MeV Xe + to 2 x 1015 cm -2. (from ref. 170)

Ion Mixing f~.c + hcp Ni AI a

I r r a d i a t i o n Ni AI a+NiAI a

AI ~ Ni NixAI Ni A] a-.NiAl

N i ~ AI a+NiAI a a~l,'c

Equilibrium NI3AI Ni A1 Ni2AI 3 NiAI3

0 10 20 30 40 50 60 70 80 90 100

at % AI

Fig. 51. Summary of microstructures in the Ni-A1 system prepared by various ion beam treatments. (from ref. 171)

Liu [188] noted that a structurally similar phase of the hcp structure was

formed by ion irradiation of multilayered films in five binary (A-B) metal

systems (Co-Au, Ti-Au, Co-Mo, Ni-Mo and Ni-Nb) where A refers to the first

entry in the alloy designation. The phases were formed in the A-rich multilayered films with overall composition between 65 at% and 80 at% A.

Further, the spacing of the close-packed planes (dcpp) of all the hcp structures

were quite similar. Their formation was attributed to the valence electron

effect. For a close-packed hexagonal structure, the minimum number of electron


states per atom, n, in the Jones' zone can be calculated by the following equation

[1891,

n = 2 -3/4(a/c) 2 [1 - 1/4(a/c)2], (4.8)

where a and c are the lattice constants of the hcp structure. According to this

calculation, the n values of these five phases are almost identical, i.e., n = 1.73 to

1.74, which is very close to the value of 1/4 = 1.75, corresponding to the well-

defined Hume-Ropthery 7/4 electron compound. The phases can therefore be

considered as metastable electron compounds [190].

It should be noted that from a crystallographic viewpoint, the hcp and fcc

structures are similar since both are built by the stacking of close-packed atomic

planes differing only in stacking order. Liu therefore states that the structure of

the ion-induced phase is always the same as, or similar to the major constituent

metal of the alloy.

The formation of metastable phases by ion irradiation of binary alloys

exhibiting positive heats of formation has also been demonstrated. Several

authors have investigated ion induced phase formation in these systems [191-

197] and Peiner and Kopitzki [198] characterized ten binary systems. In this

study, multilayered samples of ten binary metal systems of different overall

compositions were bombarded at 77K by 400 keV Kr + ions. All systems had

positive values of AHf, meaning that in thermal equilibrium there is no, or only

a limited miscibility of the components of the considered system. However, for

the systems Au-Rh, Cu-Rh, and Cu-Ir, whose components all have fcc structures,

a continuous series of single phase metastable fcc solid solutions is produced by

ion beam mixing. For the systems Au-Ir, Ag-Ir, and Ag-Rh, they obtained a

continuous series of single phase solid solutions upon ion irradiation, and for the

other systems an increased solid solubility of one component in the other was

achieved. Figure 52 shows the larger one of these solubilities for each system

versus AHf to illustrate the influence of the magnitude of AHf on the ion beam

induced solid solubility. Note that the data points of the systems whose

components have the same structures and of systems with components of

different structure follow smooth curves. Both curves exhibit a rapid decrease

from complete solubility to a solubility below 15 at% in a range of AHf of about

12 kJ/mol. However, even at large values of AHf, the solubility still has not d i sappeared .

Metastable solid solutions can also form by displacement mixing at

temperatures at which radiation-enhanced diffusion is sufficiently slow to

maintain the supersaturated solid solution phase. Tsaur et al. [191] showed that

292 G.S. WAS

ion beam mixing of multi layered Ag-Cu targets formed a continuous series of

metastable solid solutions across the phase diagram. Although the phase

diagram of the Cu-Ag system is a simple eutectic one with rather small

solubilities of Ag in Cu and Cu in Ag, irradiation produced a single phase

metastable solid solution with the fcc structure across the entire Cu-Ag system.

In studies of Au-based systems (Au-Ni, Au-Co), Tsaur et al. [191-193] also found

that a single-phase solid solution could be formed over an even wider

composition range than that achieved with splat cooling techniques. Since ion

beam mixing takes place mainly in the solid state, extended solid solutions can

be achieved in nearly immiscible systems such as Ag-Ni. Even in the binary Au-

Fe and Au-V systems which have more complex phase diagrams with a large

solubility gap and several intermetallic compounds, respectively, and the bcc

structure at the Fe- and V- rich terminal solid solutions, Tsaur et al. [193] was

able to produce metastable solid solutions across both systems using ion beam

mixing. In all cases, the lattice parameters of the solid solutions vary smoothly

with composition and show small or moderate deviations from Vegard's law

between the appropriate end-members.

100 ~ - Cu-Co"'

Au-N~

~ so

~ 6 0 Ag-RhJ

d 40 \ o \ \ (:3 Au-lt ~ Au -Os _~ 20 , , \ \ / O Ag-N,22---:CW'o~ \e~ Ag'Ru A

-i/ ~ . L _ ~ Ag-Ru A~Os

Ag

I I I 20 30 ~0

&H t [ kJ Imo l ]

Fig. 52. Irradiation-induced solid solubilities for binary metal systems of positive heats of formation vs AHf. (from ref. 198)

(iii) Ouasicrvstalline ohase formation. The most novel metastable phases

produced to date are the quasicrystalline phases, produced by ion irradiation of

specific AI alloys. These phases show long-range order, but possess forbidden

crystalline symmetries such a five- or six-fold symmetry. The phase was

discovered by Shectman et al. [199] at the National Bureau of Standards.

Quasicrystals have positional order, but are neither periodically nor randomly


spaced; instead, they are quasiperiodically spaced [200]. This means that, given

the position of one unit cell, the positions of the other unit cells are determined

according to a predictable but subtile sequence which never quite repeats.

Because these structures are highly ordered like crystals but are quasiperiodic

instead of periodic, they have been called quasiperiodic crystals, or quasicrystals

for short.

Knapp and Follsteaedt [201] and Lilienfield et al. [202] were the first to report

the ion-beam-induced formation of the quasicrystalline phase. This work was

on the AI-Mn system, but to date, many more binary, ternary and quaternary

systems have been shown to form quasicrystals under irradiation [186,187]. In

these initial experiments, the quasicrystal phase was formed by irradiating

alternating layers of AI and Mn in the composition A184Mn16 with 400 keV Xe

ions to doses of 2-10 x 1015 Xe/cm 2 at 80°C. Results showed that the icosahedral

phase forms without a separate thermal treatment at or above 80°C while the

amorphous phase forms at 60°C. The icosahedron is a regular polyhedra

possessing twenty identical triangular faces, thirty edges and twelve vertices.

The black pentagons on the surface of a soccer ba l l are centered on the vertices

of an icosahedron. This observed dependence on sample temperature suggests

that the icosahedral phase does not form within the dense ion cascade, but

rather during subsequent defect evolution. Similar results have been achieved

with freestanding AI-Fe mult i layered samples [187], indicating that both

multilayered and amorphous samples can be transformed to the quasicrystalline

phase.

In addition to the temperature window for the formation of quasicrystals in

A1-Mn, the composition of the samples has an important effect on quasicrystal

formation. Below 80 at%, and above -90 at% A1, quasicrystals could not be

formed in any of these systems. Figure 53 summarizes the composition vs

temperature data for the three systems. All the data were obtained with

implantation of 600 keV Xe to a fluence of 4 x 1015 /cm 2. As shown,

quasicrystals are formed within a well-defined composit ion and temperature region.

(iv) Amorohous phase f o r m a t i o n , Although the phase space available to an

alloy is extremely large, only one point corresponds to an absolute minimum in

free energy. This point represents the equilibrium phase. Given sufficient time,

at any temperature greater than zero, the system will find that point and settle

into the equilibrium phase. Nonetheless, there are generally other minima in the

free energy phase space which are of varying depths. These other minima

294 G.S. WAS

correspond to metastable phases. Certain of these phases exhibit compositional

short range order (CRSO) very similar to that of the equilibrium phase but

different compositional long range order. Similarly, the spatial arrangements of

the atoms on a small scale (topological short range order - TSRO) can be very

similar to the equilibrium phase but with different long range order (such as fcc

vs hcp phases). In general, there may exist many phases with CSRO and TSRO

which are nearly identical to the equilibrium phase. Common examples of such metastable phases include glasses and crystalline solids with a slightly different

unit cell than the equilibrium.

200

~ 150

~00 E

50

0 0 • • •

O 0 O~tX:~() 0 m

oooooooooloo I

,o 2*o ' 30 a t % M

O AICr quas~crystol o AIFe quoslcrystol o AIMn quostcrystal • Amorphous • Cr ysfo l l ine

Fig. 53. Temperature versus composition diagram for the A1-Cr, A1-Fe and AI- Mn systems showing the quasicrystalline forming regions. (from ref. 186)

It has been argued that in alloys with large negative heats of formation,

disruption of chemical short range order will lead to lattice destabilization and

the formation of an amorphous phase [203]. In fact, the data on ion irradiation

of intermetallic compounds supports just this sort of conclusion [168,203].

Contradicting these observations are results of electron irradiation which shows

that complete disordering often precedes the formation of an amorphous phase [176,204]. Furthermore, for intermetallic compounds such as Zr3AI or FeTi,

electron irradiation disorders but does not amorphize the compounds [206].

Irradiation with light ions produces much the same result as electron irradiation

in that the amorphous phase is difficult to form. This suggests that disruption of CSRO is not adequate for lattice destabilization and that another mechanism must

be responsible for amorphization such as topological disorder [205-209]. In fact,

the self-ion irradiation of Ni which induces a phase change from stable fcc to


metastable hcp as discussed in section 4.B.i, clearly has no chemical component

and must be a result of the topological disorder introduced into the system by

the Ni ÷ beam. A significant number of metal-metal and metal-metalloid alloys can be

rendered amorphous during implantation at sufficiently low temperature. Yet,

at present, no general theory has been developed to predict which alloys can be

expected to become amorphous. However, a set of empirical rules have been

proposed to "correlate" the tendency for a system to amorphize under irradiation

with various material parameters. These have been reviewed most recently by

Follstaedt [181] and Ziemann [182]. The rules are as follows:

R<0.59 (H~igg rule) for interstitial metalloids

Negative heat of compound formation

Simple structures rule

Structural difference rule

Solubility range of compounds/critical defect density

Each of these rules will be treated in individual sections with emphasis on their

possible significance in the amorphization mechanism. The various theories

proposed to explain ion-induced amorphization are incorporated into the

appropriate sections.

(a) H~i~e Rule

The H~igg rule [210] states that if the ratio (R) of the metalloid atom radius to

the metal atom radius satisfies R < 0.59, a compound with a simple structure will

form in which the metalloid occupies interstitial sites in a metal lattice. If R >

0.59, a simple embedment of the metalloid atoms in the crystal lattice of metals

is not possible. The occurrence of structural rearrangement processes would be

necessary, but these cannot take place within the very short lifetime of the

thermal spike. Hence, the amorphous structure initiated by irradiation is frozen

in. Shown in Fig. 54 [211], the R=0.59 lines forms a clear division between the

implanted alloys found to be crystalline compounds and those found to be

amorphous. Melt quenching studies suggest that amorphous compounds will not

be formed for R > 0.88, Fig. 54, but Grant et al. [212] show that Ni can be

amorphized by As, Sb or Bi implantation for which R = 0.96 to 1.18. Hence, the

upper limit on the size ratio is not valid for implantation-induced amorphization.

296 G.S. WAS

c O J2

t

• ~0tl

IE

0106

/

c~c, ~ , L ? ~ j . ;;y" '. /--[-~7~

/ o ~ /

/ + •

• •

/

/

+1

/ /

Q I I I

~t ; ~13 a ~ O J7

METAL A r O N I C R A O I u S [ n m ]

~ p

~ C

~ N

Fig. 54. Summary of the observations of amorphous (0,+) and crystalline (-) alloys in metals implanted with metalloid ions, shown as a function of the two atomic radii. (from ref. 211)

This atomic size, or structural criterion is augmented with a criterion based on

electronic considerations. According to Hafner [213], the tendency for glass

formation can be correlated with a high negative enthalpy of formation.

Miedema et al. [214] argue that the formation enthalpy consists of a negative

contr ibut ion, A~* corresponding to the chemical potential difference and a

posi t ive contribution Anw-s corresponding to the difference of the electron

densities at the boundary of the Wigner-Seitz cell. Using these definitions, the

criterion for the formation of amorphous metal-metalloid compound formation

by ion implantation becomes [215]

A0* < 0.75 Anw_s 1/3, (4.9)

where A~* is in volts and Anw-s is in 6 x 1022 electrons/cm 3. By this criterion

(consisting of a structural and an electronic aspect) Hohmuth et al. [216] claim

that it is possible to predict the formation of amorphous metal-metalloid alloys

after ion implantation. Andrew and coworkers [217] have treated the stability of implantation-

induced amorphous phases on the basis of the nearly free-electron approach by

Nagel and Tauc [218]. They argue that for Q = 2kf, where Q is the wave vector of

the first peak in the structure factor and kf is the Fermi wave vector, the Fermi

level falls into a minimum of the electronic density of states. In the free-

electron limit the Nagel-Tauc theory reduces to a valence electron concentration


predicting optimum glass fqrmation for a valence electron concentration = 2

eV/atom. For a small number of amorphous ion-target systems only, for which

data are available [219] this rule is satisfied. Hence, the rule is not universally

accepted.

Naguib and Kelly [220] have proposed a model based on the concept of the

thermal spike. They argue that the region surrounding the ion track in a solid

can be regarded as a small, hot disordered region which is equivalent to a liquid

and is surrounded by crystal. Crystallization occurs in an epitaxial regrowth

fashion at the l iquid-solid interface. But regrowth only occurs if the

temperature at the interface is below the solidus melting temperature, Tm and

above the temperature of crystallization, Tc. This leads to the criterion that a

substance amorphizes if To/TIn > 0.3, and remains crystalline if Tc/Tm < 0.3 [220].

They go on to complement this model with a bond-type criterion which accounts

for the nature of the bond, i.e., ionicity in the tendency for a compound to

amorphize during irradiation. This criterion states that substances with an

ionicity < 0.47 will amorphize on ion impact [220], where ionicity is defined as

ionicity = 1 - exp{-0.25(XA-XB) 2 }, (4.10)

and XA and XB are the electronegativities of atoms A and B. According to eqn.

(4.10), the bond-type is determined only by the difference ( X A - XB). Although

this rule holds for some 52 of 56 non-metallic compounds studied, the rule seems to fail for other systems [219].

(b~ Negative heat of compound formation

Alonso and Simozar [221] noted that a good correlation exists between the

heat of formation of a compound and the formation of amorphous phases in

metal-metal systems. They found that systems with large negative heats of

formation tended to amorphize under irradiation, and constructed a plot of the

ratio of the atomic radii and the heat of formation calculated using the Miedema

model [222], Fig. 55. According to Alonso and Simozar [221],alloys do not become amorphous if the heat of formation is greater than +10 kJ/mol.

However, it was demonstrated [193] recently that the amorphous structure can

be formed by ion mixing if the heat of formation is higher, e.g., Cr/Ag, Co/Cu,

Fe/Cu and Co/Au. More recently, Peiner and Kopitzki [198] have shown that

specific compositions in the Au-Ir, Au-Ru and Au-Os systems, whose heats of

formation range from +19 to +27 kJ/mol, can be made amorphous by irradiation.

298 G.S. WAS

|+1 ig s

1 I

i' i l l , f ,, #

02+

,~ tl2, /

, I /o o+ !

~a hJlw~

Fig. 55. Ratio of atomic radii versus the heat of formation of an equiatomic compound (o metal-metal, crystalline, • metal-metal amorphous, A metal- metalloid crystalline, • metal-metalloid amorphous). (from ref. 221)

(c) Simole structures rule

Hung et al. [184] proposed that ion beam mixing will result in the amorphous

phase whenever the overall composition is not close to that of a compound with

a simple crystalline structure. Conversely, when the overall film composition is

close to an equilibrium alloy with a simple structure (fcc, bcc, hcp), the

crystalline phase will be formed. This rule was constructed as a result of mixing

experiments on the A1/Pt, A1/Pd and A1/Ni systems. It was observed that

crystalline phases of simple structures, such as solid solutions or simple cubic,

can be formed while amorphous structures are formed with more complex

structures. This is explained by the short duration of the relaxation stage

following the thermal spike. The authors argue that during the relaxation

period, atoms attempt to rearrange themselves. If the relaxation time is

sufficient for precipitates to nucleate, crystalline phase formation may be

achieved. The time required for nucleation is strongly influenced by the

temperature, the crystalline structure of nulcei and the composition of the films

which have been homogenized with thermal treatments or ion beams. If the

overall composition is not close to a simple crystal structure in the equilibrium

phase diagram and there is not a strong chemical driving force (as well as

mobility) to promote significant atomic motion, crystalline phase formation may

be inhibited. Recall that Alonso and Simozar [221] concluded that the occurrence

of an amorphous alloy produced by ion mixing is strongly linked to the existence


of an equilibrium compound, and hence, with a negative heat of formation.

Although this works for many compounds, extensive experimentat ion has revealed that many alloys with simple equilibrium crystal structures (eg., NiA1,

FeTi, NiTi, CuZn, etc.) become amorphous under irradiation.

(d) Structural difference rule This rule was formulated by Liu [223,224] in 1983 and states the sufficient

conditions for producing amorphous alloy films by ion mixing of multiple alternate metal layers: (1) the constituent metals have different structures, and

(2) the composition after uniform mixing lies within the two-phase region of the equilibrium phase diagram. This rule predicts amorphous alloy formation irrespect ive of the atomic size and e lect ronegat iv i ty propert ies of the

constituents, as long as the constituents have different crystal structures.

Although Liu cites several examples of systems for which this rule is obeyed,

there are a large number for which it is not obeyed. For example, FeAI (bcc-fcc) does not amorphize after ion doses up to 40 dpa [168]. Similarly, Ni3Ti (fcc-hcp)

does not go amorphous. In fact, the c o n v e r s e of this rule often is obeyed. That

is, constituents of the same crystal structure have been found to amorphize: NiA13 (fcc), PdAI3 (fcc), several Pt-Al(fcc) alloys, and AI2Au (fcc) are a few examples. Further, it should be noted that the composition appears to play a significant role, since in the Ni-Ti, Ni-A1 and Pd-AI systems, only certain alloy

compositions amorphize under irradiation. Hence, although it provides a general

guideline, the structural difference rule is not universally obeyed. As a result,

L iu [190] has concluded that the rule is a sufficient, but not a necessary

condition.

Liu [190] proposed an extended structural difference rule based on the use of

the equilibrium phase diagram for the binary alloy under consideration. The rule states that if the overall composition is in the two-phase region of the phase

diagram, an amorphous alloy will most likely form. If the overall composition is

in or near the single-phase region of the phase diagram and the structure of this phase is not simple, an amorphous alloy is likely to be formed. Finally, if the overall composition is in or near the single-phase region of the phase diagram and the structure of this phase is simple, a crystalline phase is formed. This

model can be understood with reference to Figs. 56a and b, which are a

representative phase diagram and the corresponding free energy- composition

diagram. Regions 1, 2 and 3 refer to the single phase region where the phase is a solid solution with a simple crystal structure (fcc, bcc, hcp), a two-phase region, and a single phase region, typically an intermetallic compound which exists in a

300 G.S. WAS

narrow composition range and frequently possessing a complicated structure,

respectively. In the free energy diagram, points x, y and z refer to the

equilibrium states of the alloys having the compositions 1, 2 and 3 respectively.

Points X, Y and Z refer to the free energy of the random mixtures immediately after mixing (prompt process). Along the path toward equilibrium, metastable

states may be encountered which have free energies greater than equilibrium

but less than the random mixture. The curve labeled "amorph." refers to the

amorphous states.

To

A

L

B

I X Y Z .

A B [B]---"

Fig. 56. Representative phase diagram (a), and the corresponding free energy- composition diagram (b) (A excited state, • amorphous state, o equilibrium state) for a binary alloy. (from ref. 188)

In region 2, the transition from Y--> y requires an adjustment in composition

involving large-scale atomic movement via diffusion, which will be difficult due

to the short duration of the thermal spike and the low temperatures at which

the mixing is conducted. However, the Y --> Y' (Y' is amorphous) is polymorphic

(diffusionless transformation) and will be favored.

In region 3, both transitions, Z --> z and Z --> Z' are both polymorphic, but the

more compl ica ted ~ phase requires greater atom mobili ty and thus, its

formation will be kinetically limited. The amorphous phase will be favored.

In region 1, X --> x is polymorphic, and since the terminal solid solution always possesses a simple crystal structure with high growth kinetics and little

atomic movement, the transition can be completed within the relaxation period

of the thermal spike (10 ps).


Figure 57 is an ion-induced phase diagram constructed from the equilibrium

phase diagram and the free energy-composit ion diagrams of Fig. 56. The

appearance of the metastable MX phase can be justified by noting that the free energy curve of this phase should be similar to that of a compound, e.g., the ~/'

phase, and the transition from the random mixture to the MX state is therefore

polymorphic. Second the MX phase is of a simple structure, ie., an enlarged hcp

structure, therefore, the crystal l ization process can be completed during

q~

A+B I

relaxation.

A [B] ----- B ,Tccorhcpl ~hcc )

Fig. 57. Ion-induced phase diagram. Extended (supersaturated) solid solutions a ' and 13' are obtained from both sides of the phase diagram. As the composition approaches the middle of the phase diagram from the side A, a mixture of amorphous phase and MX phase (hcp) is formed at intermediate dose, while a mixture of an amorphous phase and 13' phase is obtained approaching from the B side. At high dose, a uniform amorphous phase is formed. (from ref. 188)

Liu presents extensive data to support these observations in each region of

the phase diagram. The rule succeeds, not only in/ explaining the amorphization

of a large number of metal combinations with different lattice structures, but also with the same lattice structure.

A set of rules related to the structural difference rule has been proposed by

Johnson et al. [30]. In their treatment, they make use of a binary constitution

diagram of an A-B alloy, Fig. 58, a schematic free energy diagram for this alloy,

Fig. 59, and the corresponding polymorphic phase diagram, Fig. 60. Note that the

To curves are obtained from the crossing of the solid free energy curve with that

of the liquid (or amorphous) curve at a given temperature. The Toa line defines the thermodynamic composi t ion limits of the or-solution. When the

concentration profile induced by mixing falls locally outside these limits, the Qt-

302 G.S. WAS

solution is superheated with respect to the liquid (amorphous) phase and is not

stable. Since melting is a local phenomenon not involving long range diffusion,

and since solids are not observed to withstand extensive superheating, it follows

that observation of an a-phase outside these composition limits represents an

unstable state. Such a state will likely melt or amorphize before thermal spike

evolution is complete.

T2 LIQUID X

B

~2

B (a) COMPOSITION C B (13)

Fig. 58. Binary constitution diagram of an A-B alloy. (from ref. 30)

(~w ~-u_(z: T:Tz

A B COMPOSITION C B

Fig. 59. Schematic free energy diagram for the alloy of Fig. 58 at temperature T1, crossing of ct and ~. curves defining the To a curve. (from ref. 30)

?_

I -

LIQUID X

', lo( % ) ',.< '/

A B COMPOSITION C B

Fig. 60. Polymorphic phase diagram corresponding to the equi l ibr ium phase diagram of Fig. 58. Dashed lines show part of the original equilibrium diagram. Solid lines are r e p r e s e n t a t i v e To -lines of each phase. The To-lines define regions of polymorphic solid formation from the l iquid state. Reg ions outs ide correspond to liquid or amorphous (polymorphic) states. (from ref. 30)

This leads to the first fundamental rule for solid phase formation. Johnson et

al. [30] assert that terminal solid solutions oc and 13 can be formed up to the limits

of the Toct and To~ curves (i.e. within the polymorphic phase diagram limits of 0c

and 13). Solutions formed outside these limits are superheated and unstable

against amorphization or melting. Secondly, intermetallic compounds with broad


equilibrium homogeneity ranges (wide polymorphic limits in Fig. 60), and low

energy interfaces with a-solution or 13-solution phases, may form in the prompt

cascade provided that their respective growth kinetics allow high growth

velocities. Compounds with narrow homogeneity range and complex chemically

ordered unit cells should not form. Finally, amorphous phases are expected

whenever the ion induced composition profile CB(z) lies outside the polymorphic limits of crystall ine phases. Amorphization may occur in addition when polymorphic limits permit compound formation but kinetics of compound

formation or growth are slow. Martin [225] proposed a theory for amorphization which is similar in nature

to that of Johnson. In this model, he adds the ballistic radiation recoil resolution

displacement jumps to thermally activated jumps to obtain an irradiation-

altered diffusion equation. The practical effect of irradiation is then to cause the

system to assume the configuration at temperature T that it would have at a temperature T' outside irradiation: T' = T(I+D'B/D'), where DB' is the ballistic diffusion coefficient, due to displacements and D' is the interdiffusion coefficient

in the absence of ballistic effects, Fig. 61. The theory predicts that irradiation of

an equilibrium alloy of two solid phases at temperature T could raise the "effective," temperature to TI', or, under sufficiently intense irradiation to T2'. At TI', the irradiated alloy would at steady state, be composed of amorphous and

crystalline phases of different compositions. Irradiation intense enough to raise

the effective temperature to T2' would produce a uniform amorphous alloy. The predictions of this theory have yet to be tested.

T(K) ,~

T I'

T ' - @ - - - - -

c

a+B

C ( % )

Fig. 61. Possible configuration of an equilibrium, two-phase alloy under irradiation at temperature T. Irradiation to an effective temperature TI' gives amorphous and crystalline phases of different composition, while more intense irradiation to an effective temperature T2' gives a single uniform amorphous phase. (from ref. 225)

304 G.S. WAS

(e) Solubility range of ¢0mpoonds / critical defect density

Brimhall [168] noted that the tendency toward amorphization of the

intermetallic compounds by irradiation correlated reasonably well with the

degree of solubility within the phases. That is, alloys with limited solubility or a

narrow compos i t iona l range show greater t endency for amorphous

transformation. This correlation is also consistent with the concept that a critical

energy or defect density must be created before the amorphous transformation

can occur. If the total free energy of the defect crystalline state becomes greater

than that of the amorphous state, a spontaneous transformation should occur.

Associated with this critical free energy is a critical defect concentration. If this

critical defect concentration can be reached under irradiation, then the crystal

should relax into the lower free energy (amorphous) state. This critical defect

concentration has been estimated at 0.02 for silicon and germanium [226].

The link between defect density and degree of solubility can be seen by

referring to the free energy diagram in Fig. 62. Compounds with no or limited

compositional range will undergo a greater increase in free energy than those

with wide compositional range. The greater increase in free energy is due to the

inability of the compound to exist in equilibrium outside the designated

compound. This is manifest in the narrow and steeply rising free energy vs

composition curves. For ordered phases (intermetallics) the increase is not only

due to point defects, but antisite defects in regions of localized nonstoichiometry.

This proposed solubility rule is very consistent with Johnson's thermodynamic

analysis [30]. Note that for NiA13, only a slight deviation from stoichiometry is

needed to result in a very large rise in the free energy. Therefore, the critical

defect density would be low for NiAl3 as compared to NiAi.

Antisite defects may play a critical role in the amorphization process since

calculations have shown that the critical defect density may be difficult to reach

accounting for only point defects [227]. However, since the defect concentration

is strongly dependent on atom mobility and this is largely unknown in

intermetallic compounds, accurate estimates of defect concentration are difficult

to determine. Further, the critical defect density will be strongly temperature

dependent with higher concentrations required at higher temperatures.

P e d r a z a [205-207] has extended this theory to include the existence of a

defect complex. Because simple point defects do not normally reach the levels

needed for amorphization during irradiation, she postulated a defect complex

consisting of a vacancy and an interstitial. The likely site for such an interstitial

is one where the chemical nature of the geometric neighbors allows a situation

resembling that in the normal ordered lattice. The role of the vacancy is to allow

for partial volume relaxation. The interstitial will also have a higher tendency


for remaining in this site if there is a vacancy nearby. Thus the formation of the complex constitutes a mechanism for relaxing local stresses while creating a center of short-range order and a focus of topological disorder under irradiation. This is what is needed for promoting a disordered structure under irradiation.

,Af

L

AI

Ni 2

7 1 I

! , i I .o,

I I - I I

- , I - , t I I 1 I

L I I I If I l i i l I 50 Ni

1600 f

1400

12OO

1000i

8 0 0 1

6001

ol 0 10 20 AI

{ N i z ~ ~ 38.

f i X,% NI3AI

' ~ ' ~ 1453'

- i i

' ' : ' : I t I I h I I ~ . , 1 30 40 50 60 70 80 90 100

ATOMIC % Ni r, di

Fig. 62. NiA1 phase diagram with hypothetical free energy diagram at the irradiation temperature. (from ref. 168)

Further support to the critical defect density idea is provided by the observation that compounds that go amorphous during irradiation do not show evidence of prior dislocation loop formation [228,229]. Although it has been assumed that the attainment of a critical defect concentration will cause an amorphous transformation, the high free energy associated with the point defects can also be relieved through the formation of dislocation structure. This

structure evolves from the initial collapse of interstitial or vacancy clusters into small loops. However, either a material goes directly to the amorphous state or forms dislocation loops.

Since greater mobility is required for the formation of dislocation loops, and the maximum defect concentration associated with the nucleation of loops in

306 G.S. WAS

irradiated metals is -10 -4 [227], almost two orders of magnitude less than that

for amorphizaticn, this indicates that defect mobility is a key factor in the

amorphization process. This observation is consistent with the ease of

amorphizat ion in intermetall ics where defect mobil i ty is low, and the

preferential formation of dislocation loops in pure metals and solid solution

alloys where the mobility is high.

Brimhall [168] explains some of the many exceptions to this rule (e.g., the

ReTa ~ phase which has a wide compositional range yet becomes amorphous

upon ion bombardment) by a low defect mobility at the irradiation temperature.

Similarly, he claims that high solubility in nickel explains why compounds on the

nickel rich side of the Ni-AI and Ni-Ti phase diagrams remain crystalline while

the low solubility of Ni or Ti in AI explain why the aluminum rich compounds

readily amorphize. Hence, when an element or phase shows very limited

solubility for another element or phase, the amorphous transformation is more

likely to occur during irradiation. In these compounds with limited

compositional range, the basic compositional unit will try to maintain itself,

resulting in a high degree of short-range order (SRO) in the amorphous phase.

Since only short-range motion and relaxation occurs at these low irradiation

temperatures, the SRO regions are highly misoriented with respect to each other.

Because the low defect mobility does not permit long-range ordering, the

amorphous structure forms.

Eridon et al. [183] argue that such short range order exists in the amorphous

phase of composition NiA13. Calculations indicate that either a disordered

crystalline (orthorhombic) structure or a disordered amorphous (no short-range

order) structure will have a significantly higher free energy than an ordered

amorphous (short-range order) structure.

Br imhal l [168] points out that the compositional range or extent of solubility

in a phase is not a fundamental physical parameter but is, in fact determined by

the combination of other factors such as bonding, atom size, and electronic

s t ructure .

(f~ Soike and temoerature effects

From the preceding discussion, it is evident that many of the proposed amorphization mechanisms rely on the existence of a cascade. Brimhall et al.

[229] irradiated NiTi with 2.5 MeV Ni + and 9 MeV Ta + and found that the

amorphous volume fraction as a function of dose in dpa exhibited supralinear

behavior, Fig. 63, which is consistent with a cascade overlap model for the

formation of amorphous zones. Simonen [230] has modeled the volume fraction


of amorphous phase as a function of dose using the cascade model as well as the

point defect model and can f i t the experimental data with either. Thus, both

models can be made to be consistent with the observed results. Nevertheless,

experiments on Ga and AI2Au show that in some cases, amorphization can occur

in the absence of cascade formation.

.=

E <~ 0.1 _g

1 0 - -

001

t/ C

0 1

D o s e (dpa)

2 5 MeV Ni *

6 MeV Ta* * •

Fig. 63. Amorphous volume fraction as a function of dose in dpa for NiTi bombarded with either 2.5 MeV Ni ÷ ions or 6 MeV Ta ++ ions. (from ref. 229)

Results of quench-c0ndensation experiments indicate that gallium may be

amorphized by ion irradiation. Goerlach et al. [231] conducted experiments

designed to determine if pure, elemental gallium can be amorphized by

irradiation and if so, whether cascades are necessary. Crystalline a-gal l ium was

bombarded with 275 keV argon ions and 200 keV He ions at T<IOK. Results

indicated that a -Ga was transformed to the amorphous phase by Ar irradiation

at very small fluences (2 x 1014 cm-2). However, He irradiation failed to produce

the amorphous phase even after the same deposited energy. This seems to

support the idea that cascades are necessary for the formation of the amorphous

phase in this element. The fact that a pure element was amorphized brings into

question many of the rules just discussed for amorphous phase formation.

308 G.S. WAS

Another significant set of experiments involved the irradiation of AI2Au.

Since both are of the same crystal structure, the structural difference rule would

predict that amorphous phase formation is not possible. However, a rule which

states that whenever a system can be forced into the amorphous state by vapor

quenching, then ion irradiation will also result in the amorphous phase, does

predict amorphization based on vapor quenching experiments by Folberth [232].

Experimentally [233] after irradiation of crystalline AI2Au at T<10K with 250

keV Ar, an amorphous phase was formed. Amorphization also occurred after

irradiation with 200 keV He at the same temperature. At 80K, irradiation with

Ar produced the amorphous phase, but irradiation with He did n o t . These

results lead to the conclusion that at very low temperatures, spikes are not

necessary to amorphize a binary system which is known to become amorphous

by vapor quenching. However, at higher temperatures, the high energy density

of cascades governs the amorphization process.

(g) Shear in~tability-drivgn am0rphization

Okamoto et al. [177,234] have conducted experiments to measure the lattice

dilation and shear elastic constant as a function of the degree of long-range

order during room temperature irradiation of several intermetallic compounds.

In these experiments, ZrAI3, FeTi and NiA1 were irradiated with MeV Kr ions at

room temperature. The lattice parameter and the degree of long-range order

was measured in TEM and the shear modulus was measured using Brillouin

scattering spectroscopy. Results showed that for ZrA13 and FeTi, a large lattice

dilation and shear modulus sof tening were observed during chemical

disordering, which was followed by amorphization, Fig. 64. The decrease in the

shear modulus in ZrAI3 and FeTi was 50% and 40%, respectively. NiAI did not

become amorphous and showed a drop in shear modulus by only 10%. The

lattice dilation in NiA1 was also smaller than in the other two compounds. The

observed linear relationship between the increase in lattice parameter and

decrease in shear modulus during irradiation is analogous to what occurs during

heating to melting [235,236]. Lattice dilation is observe.d during heating of most

materials, and it is accompanied by a decrease in elastic moduli. The strong

correlation observed between chemical disordering, lattice dilation, shear modulus softening, and amorphization suggest that solid-state amorphization is

triggered by an elastic shear instability driven by lattice dilation and chemical

disordering. In fact, Zr3A1 was amorphized by hydrogen charging without any

discernible chemical disordering [237]. The total lattice dilation at which the


(a)

( b )

(c)

0 . 0 "

-0.5

-1.0 ¢t) f -

- 1 . 5

-2.0

-2.5 0.0

0.08

0.06, t - O

, m

~ 0.04,

0.02

0.00' 0.0

0.1

0.0

a: -, -0.I o =E

,.~ ~, -0.2 I~ tll O o

,,c -0.3 u t / )

u. o -0.4

-0,5

• [ ]

[]

[]

[]

I I

0.1 0.2

Dose (dpa) 0.3

:=

[]

[] []

In [] []

[] []

[ ]

! !

0.1 0.2

Dose (dpa) 0.3

o•ee

In M m

[] O nl D D

J,

.001 .01 .1 1 10 100

Dose (dpa)

~' FeTi • NiAI

Fig. 64. Variation of the measured parameters of FeA1 and NiAI as a function of irradiation dose; (a) chemical long-range order parameter, (b) the lattice dilation, and (c) shear modulus. (from ref. 177)

310 G.S. WAS

onset of amorphization was observed by hydrogen charging was the same as in the case of Kr + irradiation-induced amorphization.

(h} Other theories

Ossi [203,238] has proposed a model he terms the segregation charge transfer

(SCT) model in which he calculates the electronic energy change associated with

segregation occurring in the thermalization stage of the cascade and relates this

quantity to the surface energy difference between the segregated and original

alloy and hence, the potential for forming an amorphous structure. The SCT

model accounts for the development of dense well-developed cascades in targets

undergoing bombardment by heavy ions. Cascades are assumed to evolve with

two separate time scales; during the prompt regime the spike volume may be

thought of as a region encompassing a few thousand atoms in extremely violent

atomic agitation. When the locally deposited energy is insufficient to displace

recoils further from their sites, delayed events dominate.

Atomic rearrangements which occur within the spike volume involve

selective migration of one of the atomic species to the spike-lattice interface,

which thereby becomes enriched in that component. The violence of cascade

mixing is not able to compensate for the composition alteration because the

composition peak develops in the neighborhood of impacting ions following the

cascade maximum, i.e., during the final fast thermalization stage of cascade

atoms. The compositional change at the spike surface induces a local variation in

spatial electronic density, subsequently relaxing towards a bulk equilibrium

value.

For an A-B alloy, the atom-atom interaction at the surface is represented by

an electronic elementary charge transfer process between two atoms, one atom

of the surface-enriched species B and one atom of the A type. Such an

interaction is governed by the condition that the segregating element behaves in

an electron acceptor way, thus giving

A(-le-) --> Ceff

B(+le-) --> Def f

where the C-D effective atom couple is considered as a microalloy cluster in

which D segregates with respect to C, corresponding to the original alloy in which

it is assumed that B segregates with respect to A. The electronic energy change

AE, is calculated using electron energies for pure elements taken to be isolated.

Segregation in both A-B and C-D alloys is studied using Miedema's parameters,


~* and nw_sl/3. Figure 65 plots A(A(~*),- the surface energy difference between alloying elements, against A(Anw_sl/3), the difference in electron densities at the boundary of the Wigner-Seitz cell, for A-B to C-D alloy transitions in amorphous and crystalline systems. The full line separating the two regimes divides the amorphous alloys, those with lower segregation strength in C-D alloys than in A- B alloys (right-hand side) from crystalline alloys (left-hand side). The dashed line separates regions of solute segregation from those of solvent segregation. For amorphous alloys, positive A(A¢~*)and ~(~nw_s 1/3) values correspond to solute segregation, while negative values are found when the solvent segregates. The opposite holds for crystalline alloys. Figures 66a and b show A(A~*)vs AE for the two classes of systems. Note that a linear correlation exists between the two quantities for both systems.

~eebc ~ l r N

+1 OIIIfe ~ e 4 g C *

C l l r ~ g l N b

O n i Z r ~ C s n k

~ O t V l w l S l i l t . I Q L U l l S l ~ .

+0.5 mint ~ C e l a

I II & I ~ N 1 1 4 t l O Q l r l l ~ y e q k

f ,Cp__~¢ w

• 0 . . . . . . . . . . . . . . . . . . . . . . . . . . .

f ea t --- , ' lq, si 0

- -0.5 xrw~v,c , c . M t ~ u i s , ®

A u C v ~ P t l a O $ O L v ( n ! $ ( I, II, Cvs* ~ N I S D O

Zr C * ~ m k F t S o t u t ( s ( ~ n .

O S* a l ~ aSeql

- 1 . 5 ' • - 0 . S - 0 , 4 - 0 . 3 - 0 . 2 -0 .1 0 +0.1 +0.2 +0 .3

,~ (An,, , ''31 (d.u.p a

Fig. 65. Calculated A ( A ¢ * ) v s A(Anw.sl /3) relation for both amorphous and crystalline systems. (from ref. 238)

3 1 2 G.S . W A S

+0.5

- O~ ~- , '

-0.5

-1

/

- 1.5 - / 0

~ r° c

o¢.z, / t ,

// /

/

,/ G.f.. / / / / /

/ ~ t ,co /

~e(eV) +0.1 +0.2 +0.3

+ 0.5 ~ , ~ , \

oi ~ \ \ ,

_~ -o.5~ J i

<3

r ~ A ,

\ , \

\ .

\ \ \

- 1.5~- I I

- - 2 t AE(eV)

-0 .9-0 .8 -0.7 -0.6 -0.5 -0 .4-0 ,3 -0.2 -0.1

Fig. 66. Calculated A ( A ¢ * ) v s AE relation of a) amorphous and b) crystalline alloys. (from ref. 238)

A physical interpretation of the model is as follows. Positive AE values for amorphous alloys mean that the charge density adjustment is possible only at the expense of a net increment in electronic energy, which contributes to destabilization of the system through freezing of a metastable disordered structure. The reverse holds for negative AE values for crystalline alloys. Segregation behavior of alloys reflects variation in the surface energy A(A¢*) between components of A-B and C-D alloys. A negative A(A¢*), i.e., a smaller difference in the surface energy between A-B alloy elements is indicative of enhanced surface atomic mobility. This reflects a decrease in atomic coordination numbers towards a situation typical of the liquid state, with many energetically equivalent local atomic configurations. In such a situation, glass formation is likely to occur via fast quenching of highly uncorrelated atomic motions. Conversely, positive A(A¢*) values correspond to a reduced surface atomic mobility. Stronger interatomic correlation favors the attainment of static configurations and thus crystallization.


Ossi [238] notes that charge transfer mechanisms generally are effective in

driving crystal instability towards glass formation. The same type of local

ordering effects found in crystals is operative in establishing compositional SRO

in liquids and amorphous materials. In turn, compositional SRO is thought to be

essential to stabilize disorder produced inside cascades. Compositional SRO

alterations are reproduced in the SCT model by surface energy changes, i.e.,

variations in A(A~*). Benyagoub and Thome [239,240] formulated a quantitative model for the

amorphization of an alloy under ion bombardment. They assume that the

crystall ine-to-amorphous transition in ion-bombarded metallic alloys generally

results from the combination of two effects: disorder production (radiation

damage) and stabilization of the disorder by the establishment of a favorable

CSRO (already existing in the alloy or brought by implanted ions). Since the

amorphous volume in the ion-bombarded system changes continuously with ion

fluence, it is clear that the transition is not global but occurs locally. They then

assume that the amorphization takes place by the formation of amorphous

islands (clusters) as soon as the concentration of defects and stabilizer atoms

locally exceed a given threshold concentration. Their model consists of a

description of the amorphous fraction at a given depth in a crystal subjected to

ion bombardment at a given temperature. Several alloy systems were studied using both heavy and light ion irradiation

over a range of temperatures. Irradiation experiments yield a sigmoidal shape

of the amorphizat ion kinetics in implantation experiments or irradiation

experiments with very light ions, while a nearly linear fluence dependence of

the amorphous fraction is observed in irradiation experiments with heavy ions.

Values of the critical ion concentration Cc and critical volumes vc of the

amorphous clusters formed can be extracted from the fits to experimental data

using this statistical representation. It is shown that Cc varies very little with

the alloy considered and is always small compared to the concentrations

required in similar alloys prepared by fast-quenching techniques.

It was also noted that at temperatures where ions and defects are frozen in

the host alloy, the values of Vc seem to depend on the nature and composition of

the alloy rather than on the mass of the irradiating ion. Further, the critical

radius of an amorphous cluster formed by ion bombardment grows as the

temperature is decreased. Also noted was that the amorphization cross section

increases with the irradiating ion mass while de, the defect density, is nearly

independent of the mass. At room temperature, the number of ion impacts

needed to amorphize a given region of the sample is generally the same as that

at low temperature but the amorphization cross section is lower, certainly due to

314 G.S. WAS

a high rate or defect recombination. The model cannot account, however, for the

irradiation of crystalline metallic alloys with heavy ions.

C. Additional microstructoral effects of ion implantation

In addition to the changes in the phase microstructure of the surface during

irradiation, changes to the microstructure of the surface such as densification,

grain growth, texturing, dislocation formation and recrystallization also occur.

(i) Densification. Densification effects are easiest to observe during ion beam

assisted deposition when the film is being applied with the assistance of an ion

beam. Since the as-deposited film is often porous, the increase in surface

mobility due to the comcomitant bombardment with an ion beam results in

significant increases in density. The density of ZrO2 films on borosilicate crown

glass using electron beam evaporation, and an ion beam of 600 eV Ar was found

to have its highest density at a beam current density of 50 ~tA/cm 2 [241]. IBAD

of CeO2 at 300°C showed a packing density increase from 0.55 to 1.0 [242].

Densification of TiN films by 30% prepared by reactive IBAD using thermal

evaporation of Ti in a N2 partial pressure of 1.3 x 10 -3 Pa, and bombarded with

40 keV Ti ions and an arrival rate ratio of Ti ions/Ti atoms of 0.014 [243]. It is

expected that similar effects occur in metallic systems.

(ii) Ion-induced grain growth. Ion induced grain growth has been observed by

seve ra l i n v e s t i g a t o r s [244-247] during irradiation of pure metals and

multilayers. Liu and Mayer [244] observed the growth of grains of pure nickel

films upon irradiation with inert gas ions, Ar, Kr and Xe in the energy range 150

to 580 keV. In their experiments, the grain size increased with dose until

saturation at about 1 x 1016 i /cm 2. They found a nearly homogeneous grain size

in the irradiated samples as compared to a wide spread in the grain size of

thermally annealed samples. They also observed a dependence of the saturated

grain size on ion species and only a weak dependence of grain size on ion dose at high doses, Fig. 67. They suggest that the localized damage caused by the

displacement spike in the vicinity of the grain boundary is the driving force for

grain growth. The observed grain growth is explained by the reordering or

growth of heavily damaged grains onto neighboring, undamaged grains. The

reduction in energy at a localized growing grain is equivalent to the difference


between the energy released from the consumed region and the energy required

to expand the grain boundary. The initially rapid grain growth can be explained

by a larger probability of damaging an entire grain when the grains are small.

As the irradiation process continues, the large grains consume the small ones

and the average grain size increases. When the average diameter of the growing

grains approaches the dimension of the damaged volume, the probabili ty of

highly damaging an entire grain by a single collision cascade is reduced, as is the

chance of growing certain grains at the expense of others. Therefore, the grain

growth rate gradually decreases with the increase of grain size.

~ 4o a

3O c

(..9 2 0

g

0

• Xe 560 keV E

o Kr 3 1 0 k e V c

Ar 2 4 0 keY v 5 0

Xe

o - o i c5

A r ~

~ 2O

g e ,0~

a m >

I I J J I i l L I I L I I

2 4 6 8 io 14 0 z 4 6 8 to

Dose (x IOJS/crn z) Dose (x IOIS/cm z)

• Kr 150 keV

o Kr 3 1 0 k e V

x Kr 5 8 0 keV

f •

,J:

o 3-

b I I

12 14

Fig 67. Average grain diameter vs ion dose for a) 240 keV Ar, 310 keV Kr and 560 keV Xe ion irradiations on polycrystalline Ni films, and for b) 150 keV, 310 keV and 580 keV Kr ion irradiation on polycrystalline Ni films. (from ref. 244)

Atwater et al. [245] studied grain growth in thin films of Ge irradiated with

Ge, Xe, Kr and Ar ions. Based on the observed time and temperature dependence

of ion beam enhanced grain growth, they proposed that Frenkel defects created

at or near grain boundaries were responsible for grain boundary mobility

enhancement. They use the linear collision cascade model for defect generation

to argue that the number of jumps across the boundary per defect generated is

between 1 and 2.5 and that the grain growth rate is proportional to the concentration of point defects, regardless of whether they are generated thermally or by an ion beam.

Recently, Alexander et al. [246] have shown an enhanced grain growth rate

during mixing of multilayered Ni-AI films as compared with co-deposited Ni-AI

316 G.S. WAS

films of the same average composition. The difference in growth rate was a

factor of 2.2, Fig. 68. An attempt to explain the observed differences based on

the heat of mixing was made using Johnson's expression for the total number of

atom jumps induced in a spike per unit length of a cylindrical thermal spike, n.

Assuming that this value is proportional to grain boundary mobility as suggested

by Liu [244], the grain size can be related to n as follows:

(D 3 - Do3)/O u FD2/AHcoh 2 {1 + C(AHmix/AHcoh)}. (4.11)

Since the AHmix = 0 for the irradiated coevaporated films, the ratio of measured

values of mobilities should be,

(D 3 - Do3)/OIML/(D 3 - Do3)/OIco = 1 + CAHmix/AHcoh. (4.12)

Given the cohesive energy and heat of mixing of a Ni-20 at% AI alloy, the ratio in

eqn (4.12) is 3.0, as compared with the measured value of 2.2. These results

indicate that the heat of mixing appears to play a role in ion induced grain

growth as well as ion beam mixing.

i000

500

. . . . . . . ! . . . . . . . . i . . . . . . . . i . . . . . . . .

Mult ickel

p o r a t e d

100 . . . . . . . . i , , , , , • ..I . . . . . . . . i . . . . . i i

10 13 10 14 10 15 10 16 i0

Ion Dose (i/cm 2)

1 7

Fig. 68. Ion induced grain growth observed in 40 nm thick Ni, Ni-20at% A1 multilayer and Ni-20at% A1 coevaporated films irradiated with 700 keV Xe +÷. (from ref. 246)


Allen and Rehn [247] argue that it is unlikely that thermally activated jumps

of point defects generated at boundaries during ion irradiation can account for

the phenomenon of irradiation-induced grain growth on the basis of qualitative

observations of the response of the microstructure of Au films during heavy ion

irradiation [247,248]. In these experiments, the orientation of several grains

and subgrains change with time, the regions rocking in and out of contrast as

their boundary structures and the orientations of their neighbors change, until

coalescence occurs. This dynamic reorientation of subgrains has been recorded

in a series of bright field images and shows the highly active concomitant

dislocation behavior, which the authors describe as a virtual "anthill" of dislocation activity.

They note that temperatures at which grain growth experiments have been

conducted, the vacancies collapse to form faulted partial dislocation loops or

stacking fault tetrahedra bounded by partial dislocations. Under the influence of

other cascades in the vicinity, the loops and tetrahedra unfault, becoming

glissile, and then glide to free surfaces or to grain boundaries. If the structure of

a particular grain boundary allows, a dislocation may pass through the boundary

or be absorbed and cause emission of a secondary dislocation into the

neighboring grain, as has been observed during plastic deformation. Such

penetration creates a step in the boundary, that is, an element of boundary migrat ion.

(iii) Texture. There have been many reports of texture effects in ion beam mixed or ion beam assisted deposition of films. Alexander et al. [246] and Eridon

et al. [175] found that mixing multilayers of Ni and A1 in the composition Ni4AI

resulted in the formation of the hcp and fcc ("/) phases. The ~/ phase had a strong

<111> texture and the hcp phase had a <001> texture. The textures were such

that the close-packed planes of both phases were parallel to the film surface.

These textures formed regardless of the angle of the ion irradiation with respect

to the film. The formation of the texture seemed to be driven by the matching

of the close packed planes rather than the channeling of the ion beam.

Ahmed and Potter [249] found that irradiation of Ni with A1 to 1.2 x 1018/cm 2

resulted in 3500,/~ grains of 13'-phase oriented with respect to the underlying fcc nickel in accord with the Nishiyama relationship [250].

The development of texture during ion beam assisted deposition can be more

effectively correlated with the channeling directions of ions in the crystal lattice

and that the density of energy deposition would be inversely related to the

depth of channeling. Thus in an fcc crystal, the ease of channeling is in the order

318 G.S. WAS

<110>, <200>, <111>. Bradley et al. [251] have developed a model to explain the

development of preferred orientation due to low energy ion bombardment

during film growth which is based on the difference in sputtering yields for

different orientations rather than reorientation during recrystallization. Both

effects are, of course, based on the same phenomena of the variation of energy

density with channeling direction. In this model, crystallites with high

sputtering orientations are removed more rapidly and newly deposited material

grows epitaxially on the low sputtering yield orientations.

Smidt [4] summarizes the observations of ion beam induced texture

development as follows: Thin films of PVD deposited materials normally deposit

with the planes of highest atomic density parallel to the substrate so fcc films

have a <111> texture, bcc films have a <110> texture and hcp films have a

<0002> texture (for ideal c/a ratios). The easiest channeling directions in each

structure are as follows:

~c : <110>,<100>,<111>

bcc :<111>,<100>,<110>

h c p : < l l 2 0 > , <0002>

Ion bombardment causes a shift in the preferred orientation to alignment of the

easiest channeling direction along the ion beam axis. Thus, an ion beam at

normal incidence on an fcc film will cause a shift in orientation from <111> to

<110> texture. A beam incident at an angle will produce a different texture

depending on the crystallography. The texturing effect appears to be most

sensitive to high energy beams because of the larger volume affected per ion

and the deeper penetration.

(iv) Microstructural instability: Ion implantation can also induce a high density

dislocation network and induce recrystallization which can then affect the

distribution of the implanted specie. Ahmed and Potter [249] performed a study

of 180 keV A1 implantation into pure Ni at 25°C and. at elevated temperatures

(300°C - 600°C). At elevated temperatures, individual dislocation loops

dominate the microstructure at the lowest fluences (-1015 cm-2). These loops

bound collections of interstitial atoms or vacancies, defects caused by the

energetic AI ions penetrating the nickel structure and displacing atoms from

their lattice sites. The loops climb with further implantation, intersect and react

with other loops, and form complex dislocation networks after a dose of 2.1 x


1017 Al/cm 2. By a fluence of 3 x 1017 cm -2, three dimensional aggregates of

vacancies are present. The composition profiles at room temperature, 300 and 600°C to doses of 6 x

1017 cm -2 and 1.2 x 1018 cm -2 are shown in Fig. 69. Note that there is little difference with temperature. However, at doses in excess of 1.5 x 1018 cm -2, gross changes in the implanted distribution occur with the profile flattening and a considerable amount of A1 transported to greater depths, Figs. 70 and 71. The same occurs following aging of room temperature implantations at 600°C for 15 min. The microstructures developed at depths greater than the range of the 180

keV AI + ions, ~1000/~, play an important role in determining the stability of the implanted concentration profiles.

5O

40

<

~zo

10

• 2 5 ° C 1.2 x 1018 ions/cm 2 • 3 0 0 " C

1 0 0 0 2 0 0 0 3 0 O O

D e p t h 1,~1

Fig. 69. Composition profiles from specimens implanted to two fluences, as inf luenced by implantation temperature or aging at 600°C after 25°C implantation. (from ref. 249)

?0

~eo 5G

40 o

211

I C <

7 0

60

• e ~ 2 5 " C 0 50 o 5 0 0 " C

c 4 0

"' i 1 0

Depth ( A )

Fig. 70. Aluminum concentration p lot ted versus depth from a specimen implanted to f luences of 2.4 x 1018 A l + / c m 2 at 25°C and 500°C. (from ref. 249)

F ig .

- - - - RoOm ~ r a t u m - - 5 0 0 " C / /

J

4 I

1 2

F t u e n c e x 10 - l e l o n s / c m 2

71. Peak a l u m i n u m concentration plotted versus fluence for implantation at 500°C. (from ref. 2 4 9 )

320 G.S. WAS

Dislocat ion loops are present at depths near 3000/~ fol lowing room

temperature implantation. These loops are 50-100]k in diameter and their number density increases with fluence, reaching - 4 x 1016 cm -2 at 3 x 1018 i/cm-

2 These are determined to be Frank faulted loops. However, the dislocations

behind the implanted layer are removed when the material is heated to 600°C.

This occurs by recrystallization which is also responsible for the redistribution of

implanted AI. The following describes the processes occurring.

Following room temperature implantation, an amorphous phase extends to a

depth of -1600/~. Small crystal of 13' and ), extend from 1600]k to -3000/~ and

from ~3000/~ to ~4000/~, respectively. Dislocations and dislocation loops extend

beyond this to depths of >8000/~, as shown in Fig. 72a and b. Aging at 600°C

following room temperature implantation or implanting at high temperatures

causes recrystallization of the fine grain structure to depths of -8000/~ to

~10,000/~. In both instances, a luminum atoms must move through relatively

pure nickel to accomplish the redistribution which is only possible if some fast

diffusion process occurs. This is afforded by the small grains which form upon

recrystallization of the heavily dislocated region beyond the implanted layer and

provide high angle grain boundaries for abnormally fast diffusion. The

composi t ion reaches a plateau by virtue of the limited extent of the recrystallization. Also note, Fig. 73, that the redistribution only occurs above a

threshold dose indicating the role of the radiation damage in the recrystallization

process. This example serves to tie together the roles of the implanted specie,

the character of the radiation damage and the processes (recrystallization and

abnormally fast diffusion) that can be affected by implantation.

A final example of the interplay between phase stability, amorphization and

irradiation microstructures is the observation of ion induced dendritic growth

upon phase transition in Ni-Mo. Huang et al. [252] irradiated multilayered films

of Ni and Mo with 200 keV Xe at -77°C and 25°C. Dendrites were observed in the Ni65Mo35 and Ni55Mo45 films irradiated to an ion fluence of 7 x 1014 Xe/cm 2

at -77°C, Fig. 74. Analyses by selected area diffraction indicated that the

branches of the dendrite were crystalline while the matrix was partially

amorphized. Since a larger ion dose amorphized the entire structure, the film

must have been at a critical state of the crystal l ine- to-amorphous phase

transition. The authors argue that since bulk diffusion in a solid film is hard to

realize under the given experimental conditions, the diffusing species would

then be the atoms, while the nucleus acted as the trap. During growth, other

nuclei would be formed and the growth of these nuclei was limited by the

existence of others. Thus growth can be characterized as self-limited, due to the superimposition of individual diffusion fields.

ION B E A M M O D I F I C A T I O N O F METALS 321

I ~ ' Am°f~°~$E~"-mA~";~u'°n" nt~r I~I "" { :~ ', ...to*,, .,: .".: 6 0 1 " / / / : ~ I .LX.~."Wh"~,~ ' . / ' e l ol. oopl.',:....--.l.,..~.'.

:;-)~ -~"~' ~.' 7: :. :.:....;~ %:-.:: 4 0 / / / / ~ ' . , . ~ - .~ ' . ' . . . .~ . ; ;... :.,-:: ~ / / / ' / ~ , ~ ~ - ~ :,~:~:,-; .;.: .. :.-:.: .~ ; : : , , ~.

~o, ~ ~.,~, ~., ,:. ::..;~.; :,~:?;.iz;..,.:. .. • ~- ' , . . . . . . . . . . . , : . . . ; . .~ ." ..

I ~ ; / / / / / ~ ~ ' % . . - . . . : - . . . ' . : ........... ~. 0

( o )

~ ' ~ i : ~ ~ ? ~ r - - ~ - N i A t T'-Ni3At( . iRecrystotti~d J ~ I

4O

,0 , . ~ . V ~ A ~ o; <z

0 1600 3200 4800 6400 8000

D e p t h ( A )

(b)

Fig. 72. Schematic representation of the microstructure observed experimentally as a function of depth: (a) in the room temperature implantation condition, and (b) after a few minutes at 600°C, for fluences > 1.5 x 1018 i/cm 2. (from ref. 249)

6 ¢

5C

4 C

3O

2 0

~0;

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , .

2-~ ,o' - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.2 II 10 III 0 I -- T . . . . . , _ 2 _ . _ : 0 , . . . . . . . . . . .

T" "~1

I I I I I I I I I I I I i i J 1.5 2 3 4 5 6 7 8 9 10 15 20 25 30 40

A g i n g t i m e (x 1 0 ~ s )

Fig. 73. Aluminum concentration versus time at 600°C for fluences (ions/cm 2) irradiated. The phases observed in the implanted layers, symbols on curves, and those expected based on the equilibrium diagram, right side ordinate, are both shown. (from ref. 249)

322 G.S. WAS

Fig. 74. Observed fractal pattern (Ni55Mo45) precipitated from an amorphous matrix with a dose of 7 x 1015 Xe+/cm 2 (marker bar indicates 2 I.tm). (from ref. 252)

5. Summary

The modification of metals with ion beams can be done in several ways. This

paper discussed the most prominent and most commercia l ly promising

techniques: direct ion implantation, ion beam mixing, ion beam assisted

deposition and plasma source ion implantation. Each has its advantages as well

as its drawbacks. However, the principles by which compositional and

microstructural tural changes are caused are essentially the same.

The compositional changes induced in a metal under ion bombardment are a

result of a number of complex processes occurring simultaneously, on of the

prime effects is the relocation of atoms in the solid caused by recoil

implantation and cascade mixing. However, the kinetics of the relocation

process is not only ballistically driven, but is also a function of the elements

involved, giving rise to so-called "chemical effects." The creation of excess point

defects and new defects types gives rise to enhanced diffusion termed

radiation-enhanced diffusion. The preferential participation of one defect over

another in the flux of defects to sinks at elevated temperatures, gives rise to

radia t ion- induced segregation. The measurements of radia t ion- induced


segregation will be influenced by the process of Gibbsian adsorption which is

the readjustment of the surface composition of a homogeneous alloy in an effort

to minimize the free energy of the system. Added to this already extensive list

is the process of sputtering or ejection of atoms from the target by the incoming

ions. This can also take the form of preferential sputtering where the ejection of elements in a multicomponent alloy are unequal. Taken together, these

physical processes present a challenge in determining the composition profile in

an alloy under irradiation. Nevertheless, the preceding sections have shown

that great str ides have been made in understanding these processes

individually as well as synergistically. However, this is only half the story - the

other being the development in microstructure.

Ion bombardment has been shown to induce the precipitation of second

phases. Subsequent irradiation can either cause the precipitates to grow or

dissolve, depending on a great many factors. Perhaps of greatest interest is the

discovery that ion bombardment can induce the formation of metastable phases. This generally occurs by one of four types of transformation: order <-->

disorder, crystal structure A --> crystal structure B, crystal structure A <-->

amorphous, and crystal structure A --> quasicrystalline. Theories for the

formation of metastable phases involve the size of the implanted ion relative to

the size of the atoms of the host, the sign of the heat of compound formation,

the size and complexity of the unit cell, the solubility range of compounds, the

density of defects in the alloy and the characteristics of the alloy which allow

accommodat ion of the point defects into lower energy extended defect

structures. Finally, changes to the microstructure directly, such as densification,

grain growth, texture and dis locat ion structure, all occur under ion

bombardment. While not present in as integrated a package as the processes

governing composi t ional changes, the preceding sections show that much

progress has been made toward understanding of microstructural changes under ion bombardment.

From a pract ical point s tandpoint , the interest in unders tanding

composit ional and microstructural changes in metals an.d alloys is for the

purpose of altering physical and mechanical properties. Since these properties

are a strong function of composition and microstructure, property improvement by ion bombardment techniques will only come through an understanding of

the effect on composition and microstructure. Hence, the stage is set for

significant progress in improving physical and mechanical properties by ion implantation of metals and alloys.

324 G.S. WAS

Reference~

1. J .W. Mayer, L. Eriksson and J. A. Davies, Ion Imolantation in Semiconductors, Academic Press, New York, 1970.

2. Ion Beam Processing of Adv~lnc¢~l Electric Materials, Vols 45 & 147, Materials Research Society, Pittsburgh, PA 1985 & 1989.

3. G. Dearnaley, ReD. Prog. Phy~,, 32, 405 (1969). 4. F. Smidt, International Materials Reviews, in press. 5. J .R. Conrad, J. L. Radtke, R. A. Dodd, F. J. Worzala and N. C. Tran, J. ADol.

Phvs., 62, No. 11, 4591 (1987). 6. G.H. Kinchin and R. S. Pease, Ren. Progr. Phys,, 18, 1 (1955). 7. P. Sigmund, J. Appl. Phys., 50, No. 11, 7261 (1979). 8. P. Sigmund and A. Gras-Marti, Nucl. Instr. Meth.. 182/183, 25 (1981). 9. A. Gras-Marti and P. Sigmund, Nucl. Instr, Meth., 180, 211 (1981). 10. J. Lindhard, M. Scharff and H.E. Schiott, Kgl, Danske Videnskab. Selskab

Ma~,-Fys. Mcdd.. 33, No. 14, 1 (1963). 11. K.B. Winterbon, P. Sigmund, and J.B. Sanders, Kgl. Danske Videnskab,

Selskab Mat.-Fys, Medd., 37, No. 14, 1 (1970). 12. Z.L. Liau, J.W. Mayer, W.L. Brown and J. M. Poate, J, Appl, Phys,, 49, 5295

(1978). 13. B .M. Paine, J. Appl, Phys,, 53, No. 10, 6828 (1982). 14. S. Mantl, L. E. Rehn, R. S. Averback and L. J. Thompson Jr., N0el. Instr,

Meth., B7/8, 622 (1985). 15. B .W. Auner, Y.-T. Cheng, M. H. Alkisi and K. R. Padmanabhan, Presented at

the Materials Research Symposium Fall Meeting, Symposium A, paper A3.5, Boston, November, 1989.

16. M.L. Roush, O. F. Goktepe, T. D. Andreadis and F. Davarya, Nucl, Instr,, Me~h,, 194, 611 (1982).

17. U. Littmark, Nucl. Instr, Meth,, B7/8, 684 (1985). 18. H . H . Andersen, .Appl. Phys., 18, 131 (1979). 19. S. Matteson and M.-A. Nicolet, Ann. Rev. Mater. Sci., 13, 339 (1983). 20. P. Sigmund and Gras-Marti, Nucl. Instr. Meth,, 168, 389 (1980). 21. S. Matteson, J. Roth and M.-A. Nicolet, Radiat. Eft., 4._2_2, 217 (1979). 22. S. Matteson, B. M. Paine, M. G. Grimaldi, G. Mezey and M.-A. Nicolet, Nucl.

Instr, Meth,, 182[183, 43 (1981). 23. H. Westendorp, Z. L. Wang and F. W. Saris, N~lcl. Instr. Meth., 194, 453

(1982). 24. Z .L . Wang, J. F. M. Sestendorp, S. Doorn and F. W. Saris, in Metastable

Materials Formation by Ion Implantation, S. T. Picraux and W. J. Choyke, eds., Elsevier, New York (1982) p. 59.

25. S .T . Picraux, D. M. Follstaedt and J. Delafond, in Metastable Materials Formation bY Ion Implantation, S. T. Picraux and W. J. Choyke, eds., Elsevier, New York (1982) p. 71.

26. B . M . Paine and R. S. Averback, Nucl. Instr, Meth., .B7/8, 666 (1985). 27. C. Fu-Zhai and L. Heng-De, Nucl. Instr. Meth., B7/8, 650 (1985).


28. F. d'Heurle, J. E. E. Baglin and G. J. Clark, J, Appl. Phys.. 57, No. 4, 1426 (1985).

29. Y.-T. Cheng, M. Van Rossum, M.-A. Nicolet and W. L. Johnson, Appl. Phys. Lett., 45, No. 2, 185 (1984).

30. W.L. Johnson, Y.-T. Cheng, M. Van Rossum and M.-A. Nicolet, Nucl. Instr. Meth., 137/8, 657 (1985).

31. T .W. Workman, Y.-T. Cheng, W. L. Johnson and M.-A1. Nicolet, Appl. Phys. Lett., 50, No. 21, 1485 (1987).

32. Y.-T. Cheng, T. W. Workman, M.-A. Nicolet and W. L. Johnson, in Beam-Solid Interactions and Transient Processes. vol. 74, Materials Research Society, Pittsburgh (1987) p. 419.

33. E. Ma, T. W. Workman, W. L. Johnson and M-A. Nicolet, Appl, Phys. Lett., 54, No. 5, 413 (1989).

34. S. Matteson, B. M. Paine and M.-A. Nicolet, Nucl. Instr. Meth., 182/183, 53 (1981).

35. T. Diaz de la Rubia, R. S. Averback, R. Benedek and W. E. King, Phvs. Rev. L¢tt,, 59, No. 17, 1930, (1987).

36. R.P. Webb, D. E. Harrison, Jr. and K. M. Barfoot, Nucl. Instr. Meth., B7/8, 143 (1985).

37. E. Ibe, N~lcl. Instr. Meth., B39, 148 (1989). 38. R. Sizmann, J. Nucl. Mater., 69&70, 386 (978). 39. H. Wiedersich, Radiat. Eft., 1__22, 111 (1972). 40. S. Matteson, J. Roth and M.-A. Nicolet, Radiat. Eft., 4..22, 217 (1979). 41. N.Q. Lain, S. J. Rothman and R. Sizmann, Radiat. Eft., 23, 53 (1974). 42. Y.-T. Cheng, X.-A. Zhao, T. Banwell, T.W. Workman, M.-A. Nicolet and W.L.

Johnson, J. Appl. Phys., 60, No. 7, 2615 (1986). 43. G.J. Dienes and A. C. Damask, ~I, Appl, Phy~,, 2_..99, 1713 (1958). 44. S.M. Myers, Nucl. Instr. Meth., 168, 265 (1980). 45. D. Peak and R. S. Averback, Nucl. Instr. Meth., B7/8, 561 (1985). 46. B. Rauschenbach, Phys. stat. sol. (a), 102, 645 (1987). 47. L .E. Rehn and P. R. Okamoto, Nucl. Instr. Meth.. B29, 104 (1989). 48. P .R. Okamoto and H. Wiedersich, J. Nucl. Mater., 53, 336 (1974). 49. R.A. Johnson and N. Q. Lam, Phy~, Rev, B, 13, No. 10, 4364 (1976). 50. R.A. Johnson and N. Q. Lain, J. Nucl. Mater.. 69&70, 424 (1978). 51. L.E. Rehn, P. R. Okamoto, D. I. Potter and H. Wiedersich, J. Nucl. Mater., 74,

242 (1978). N. Q. Lain, P. R. Okamoto and R. A. Johnson, J. Nucl. Mater., 78, 408 (1978). 52.

53. A.D. Marwick, J. Phys. F: Metal Phys., 8, No. 9, 1849 (1978). 54. P.R. Okamoto and L. E. Rehn, J, Nu¢l, Mo¢er,, 83, 2 (9179). 55. A.D. Marwick, R. C. Piller and P. M. Sivell, J. Nucl. Mater., 83, 35 (1979). 56. H. Wiedersich, P. R. Okamoto and N. Q. Lam, J. Nucl. Mater,, 83, 98 (1979). 57. H. Wiedersich, in Physics of Radiation Effects in Cry~tal~, R. A. Johnson and

A. N. Orlov, eds., Elsevier Sci. Pub. B.V. (1986) p. 225. 58. H. Wiedersich and N. Q. Lam, in Phase Transformations During lrr~diati0n,

F. V. Nolfi, Jr., ed., Applied Science Publishers, LTD, New York (1983) p. 1. 59. R.C. Piller and A. D. Marwick, J. Nucl. Mater,, 83, 42 (1979).

326 G.S. WAS

60. L.E. Rehn, P. R. Okamoto, D. I. Potter and H. Wiedersich, in Effects of Radiation on Structural Materials, ASTM STP 683, J. A. Sprague and D. Kramer, eds., American Society for Testing and Materials, Philadelphia (1979) p. 184.

61. A.D. Marwick and R. C. Piller, Radiat. Eft,, 47, 195 (1980). 62. L.E. Rehn, in Metastable Materials Formation by I0n Implantation, S. T.

Picraux and W. J. Choyke, eds., Elsevier Science Publishing Company, New York (1982) p. 17.

63. R.S. Averback, L. E. Rehn, W. Wagner, H. Wiedersich and P. R. Okamoto, Phvs. Rev, B, 28, No. 6, 3100 (1983).

64. L .E. Rehn, P. R. Okamoto and H. Wiedersich, J. Nucl. Mater., 80, 172 (1979). 65. T. Muroga, P. R. Okamoto and H. Wiedersich, R~di~lt, Eff. Lett., 68, 163

(1983). 66. L. Kornblit and A. Ignatiev, J. Nucl, Ma~er., 126. 77 (1984). 67. H.W. King, in Allovin~ Behavior and Effe¢~ in Concentrated Solid Solutions,

T. B. Massalski, ed., Gordon and Breach, New York (1965) p. 85. 68. J . E . Hobbs and A. D. Marwick, "Measurements of Radiation-Induced

Segregation and Diffusion in an Ion Irradiated Alloy Using Implanted Manganese," AERE-Rl1528, UKAEA-HarwelI, Nov. 1984.

69. J .M. Titchmarsh and I. A. Vatter in Radiation-Induced Sensitisation of Stainless Steels, D. I. R. Norris, ed., Berkeley Nuclear Laboratories, Berkeley, Gloucestershire, GL13 9PB (1987) p. 74.

70. A.D. Marwick and R. C. Piller in I0n Beam Modification of Materials, R. E. Benesen, E. N. Kaufman, G. L. Miller and W. W. Scholz, eds., North-Holland, New York (1981) p. 121.

71. T.R. Anthony in Atomic Transoort in Solids and Liquids, A. Lodding and T. Lagerwall, eds., Zeitschrift fiir Naturforschung, Tiibingen (1971) p. 138.

72. L .E . Rehn and H. Wiedersich in Surface Alloying by Ion, Electron and Laser Beam~, L. E. Rehn, S. T. Picraux and H. Wiedersich, eds., American Society for Metals, Metals Park, OH (1986) p. 137.

73. K.-H. Robrock in Phase Transformations Durin~ Irradiation, F. V. Nolfi, Jr., ed., Appl. Sci. Publishers, LTD, New York (1982) p. 115.

74. H. Wiedersich, P. R. Okamoto and N. Q. Lam in Raidation Effects in Breeder Reactor Structural Materials, M. L. Bleiberg aod I. W. Bennett, eds., AIME, New York (1977) p. 801.

75. H. Wiedersich and P. R. Okamoto in Interfacial Segregation. W. C. Johnson and J. M. Blakely, eds., American Society for Metals, Metals Park, OH (1978) p. 405.

76. P.D. Dederichs, C. Lehmann, H. R. Schober, A. Scholz and R. Zeller, J. Nucl. Mater., 69&70, 176 (1978).

77. L.E. Rehn, P. R. Okamoto, R. S. Averback, W. Wagner and H. Wiedersich, Scr. Metall.. 16, 639 (1982).

78. I. Potter and A. W. McCormick, Acts MetMI., 27, 933 (1976). 79. P. Wynblatt and R. C. Ku in Interfacial Segregation, W. C. Johnson and J. M.

Blakely, eds., American Society for Metals, Metals Park, OH (1979) p.l15. 80. N.Q. Lam and H. Wiedersich, Nuql, Instr, Meth., B18, 471 (1987).

99. 100. 101. 102.

104. 105. 106.

107.

108. 109. 110.


81. N.Q. Lam, H. A. Hoff, H. Wiedersich and L. E. Rehn, Surf. Sci., 149, 517 (1985).

82. N.Q. Lam, H. A. Hoff and P. G. Rrgnier, J. Vac. Sci. Technol., A3, 2152 (1985).

83. M.J. Kelley, P. W. Gilmore and D. G. Swartzf~iger, J, Vac, Sci, Technol,, 17, 634 (1980).

84. P. Sigmund, Phvs. Rev., 184, 383 (1969). 85. P. Sigmund, Phvs. Rev., 187, 768 (1969). 86. P. Sigmund, in Soutterin~ bv Particle Bombardmcm I, Springer-Verlag,

New York (1981) p. 9. 87. H.F. Winters, in Radiation Effects in Solid Surfaces, M. Kaminsky, ed.,

American Chemical Society, Washington (1976) p. 1. 88. J. Lindhard, V. Nielsen, M. Scharff and P. V. Thomsen, Kgl. Danske

Videnskab. Selskab. Mat.-Fys. Medd,, 33, No. I0, 1119119 (1963). 89. J. Lindhard, V. Nielsen and M. Scharff, K~I. Danske Videnskab. Selskab.

Mat.-Fvs. Medal,,36, No. 10,1 (1968). 90. E .S . /Vlashkova and V. A. Molchanov, Radiat. Eft., 108, 307 (1989). 91. Y. Yamamura, N. Matsunami and N. Itoh, Radiat, Eft,, 7, 65 (1983). 92. A. Oliva, R. Kelly and G. Falcone, Nucl. Instr. Meth., B19/20, 101 (1987). 93. R. Kelly, Nucl. Inst, Meth., B18, 338 (1987). 94. G. Falcone, Radiat. Eft. Lett., 85, 75 (1984). 95. G. Falcone, R. Kelly and A. Oliva, Nucl. Instr. Meth,, B18, 399 (1987). 96. G.N. Van Wyk and A. H. Lategan, Radiat. Eft, Lett., 68, 107 (1982). 97. R. Kelly and D. Harrison, Mater. Sci. Engin,, 69, 449 (1985). 98. H. Wiedersich, H. H. Andersen, N. Q. Lam, L. E. Rehn and H. W. Pickering, in

Surface Modifi~l¢ion and Alloyin_~, J. M. Poate, G. Foti and D. C. Jacobson, eds., NATO Series on Materials Science, Plenum Press, New York (1983) p. 261. P. Sigmund, Nucl. Instr, Meth,, B27, 1 (1987). G. Falcone and P. Sigmund, Appl. Phys.. 25, 307 (1981). N. Q. Lam, G. K. Leaf and H. Wiedersich, J. Nucl. Mater., 88, 289 (1980). N. Q. Lam and H. Wiedersich, in Metastable Materials Formation by Ion Implantation, S. T. Picraux and J. W. Choyke, eds., North-Holland, New York (1982) p. 35.

103. L. E. Rehn, N. Q. Lam and H. Wiedersich, Nucl. Instr. Meth,, B7/8, 764 (1985). R. Shimizu, Nucl. Instr, Meth., B18, 486 (1987). H. Shimizu, M. Ono and K. Nakayama, Surf. Sci., 36, 817 (1973). K. Goto, T. Koshikawa, K. Ichimura and R. Shimizu, in Proc. 7th Int. Vac. Cong. and 3rd Int. Conf. on Solid Surfaces, Vienna (1977) p. 1493. R. Shimizu and T. Okutani, Proc. 4th Symp. on Ion Sources and Applications Technology/1980, Ionics., Tokyo (1980) p. 273. M. Shikata and R. Shimizu, Surf. Sci., 97, L363 (1980). T. Okutani, M. Shikata, R. Shimizu, Surf. Sci., 99, L410 (1980). O. G. Swartzfager, S. B. Ziefecki and M. J. Kelly, J. Vac. Sci. Technol, 19, 185 (1981).

328

111. 112. 113. 114, 115. 116.

117.

118. 119.

120.

121.

122.

123. 124. 125. 126. 127. 128.

129.

130. 131.

132. 133.

134.

135. 136. 137. 138.

G.S. WAS

Ri-Sheng Li, T. Koshikawa ans K. Goto, Surf. Sci.. 121, L561 (1982). T. Koshikawa, Appl. Surf. Sci., 22/23, 118 (1985). H.J. Kang, R. Shimizu and T. Okutani, Surf. Sci., 11~, L175 (1982). N. Q. Lam and H. Wiedersich, J. Nucl. Mater., 103/104. 433 (1981). N. Q. Lam and G. K. Leaf, J. Mater. Res., 1, 251 (1986). L. E. Rehn and P. R. Okamoto, in Phase Transformations During Irradiation. F. V. Nolfi, Jr., ed., Applied Science Publishers, New York (1983) p. 247. S. G. B. Mayer, F. F. Milillo and D. I. Potter, in High-Temoerature Ordered Intermetallic Alloys, C. C. Koch, C. T. Liu and N. S. Stoloff, eds., vol. 39 Materials Research Society, Pittsburgh (1985) p. 521. H. Wiedersich, Rad. Eft., 101, 21 (1986). K. C. Russell, in Prog. in Materials Science, J. Christian, P. Haansen and T. B. Massalski, eds., 28, No. 3/4, Pergamon Press, Oxford (1984) p. 229. G. Martin, R. Cauvin and A. Barbu, in Phase Transformations Durin~ Irradiation, F. V. Nolfi, ed., Applied Science Publishers, New York (1983) p. 46. H. J. Frost and K. C. Russell, in Phase Tran~fgrmations Durin~ Irradiation. F. V. Nolfi, ed., Applied Science Publishers, New York (1983) p. 75. A. J. Ardell and K. Janghorban, in Ph~l~¢ Transformations Durin~ Irradiation, F. V. Nolfi, ed., Applied Science Publishers, New York (1983) p. 291. J. L. Katz and H. Wiedersich, J, Colloid. Interface, 2, 351 (1977). M. Mruzik and K. C. Russell, I, Nucl. Mater., 78, 343 (1978). S. I. Maydet and K. C. Russell, I, N0¢1, Mater., 64, 101 (1977). R. Cauvin and G. Martin, Phys. Rev., B23, 3322 (1981). H. Wiedersich, P. R. Okamoto and N. Q. Lam, J. Nucl. Mater. 83, 98 (1979). N. Q. Lam, P. R. Okamoto, H. Wiedersich and A. Taylor, Metall. Trans., 9A, 1767 (1978). K.-H. Robrock and P. R. Okamoto, in Comportement Sous Irradiation des Materiaux Metalliques et des Comoosants des Coeuis des Reacteurs Rapides, J. Poirier and J. M. Dupuoy, eds., Commissariat a l'Energie Atomique, Gif-sur-Yvette, (1979) pp. 57-60. H. R. Brager and F. A. Garner, J. Nucl. Mater., 73, 9 (1978). H. R. Grager and F. A. Garner, in Effeet~ 9f RadiatiQn Qn Structural Materials, J. A. Sprague and D. Kramer, eds., American Society for Testing and Materials, ASTM STP 633, Philadelphia (1979) p. 207. H. R. Brager and F. A. Garner, ~I. Nucl. Mater., 116, 267 (1983). U. K. Sethi and P. R. Okamoto, in Phase Stability During Irradiation, J. R. Holland, L. K. Mansur and D. I. Potter, eds., The Metallurgical Society of AIME, Warrendale (1981) p. 109. T. M. Williams, R. M. Boothby and J. M. Titchmarsh, in Radiation Induced Sensitization of Stainless Steel, D. I. R. Norris, ed., Berkeley Nuclear Labs., Berkeley, Gloucestershire, GL13 9PB (1987) P. 116. E. H. Lee, A. F. Rowcliffe and E. A. Kenik, ~I, Nod, Mater.. 83, 79 (1979). R. A. Nelson, J. A. Hudson and D. J. Mazey, J, Nu¢I, Mater,, 4__44, 318 (1972). K. C. Russell, J, Nucl. Mater., 83, 176 (1979). C. F. Bilsby, ~I, N0¢1. Mater,, 55, 125 (1975).

139.

140. 141 142 143 144 145 146 147 148.

149. i50.

151.

152. 153.

154. 155. 156. 157.

158. 159. 160. 161.

162. 163.

164. 165. 166. 167.

168. 169. 170. 171. 172.

173.


M. Baron, A. Chang and M. L. Bleiberg in Radiation Effects in Breeder Reactor Structural Materials, M. L. Bleiberg and J. W. Bennett, eds., The Metallurgical Society of AIME, Warrendale (1977) p. 395. A. D. Brailsford, J. Nucl. Mater.. 91, 221 (1980). P. Wilkes, J. Nuel. M~ter,, 83, 166 (1979). R. Cauvin and G. Martin, I. Nucl. Mater., 83, 67 (1979). I. M. Lifschitz and V. V. Slyozov, J. Phvs. Chem. Solids, 19, 35 (1961). C. Wagner, Z. Electrochem., 65, 581 (1961). D. I. Potter and H. A. Hoff, Acta Metall., 24, 1155 (1976). D. I. Potter and D. G. Ryding, J. Nucl. Mater,, 71, 14 (1977). D. I. Potter and H. Wiedersich, J. Nucl. Mat¢r,, 83, 208 (1979). D. I. Potter, P. R. Okamoto, H. Wiedersich, J. R. Wallace and A. W. McCormick, Acta Metall., 27, 1175 (1979). K. Urban and G. Martin, Acta Metall., 30, 1209 (1982). A. Vom Felde, J. Fink, Th. Miiller-Heinzering, J. Pfliiger, B. Schurer, G. Linker and D. Koletta, Phys. Rev, Lett,, 53, 922 (1984). C. Templier, C. Jaouen, J-P. Riviere, J. Delafond and J. Grilhe, Comoter Randus, 299, 613 (1984). A. Luukainen, J. Keionen and M. Erola, Phvs. Rev.. B~2, 4814 (1985). W. J~iger, R. Manzke, H. Trinkous, R. Zeller, J. Fink and G. Crecelius, Rad. Eft,, 78, 315 (1983). R. C. Birtcher and W. Jager, Ultramicroscopy, 22. 267 (1978). R. C. Birtcher and W. J~iger, Nucl. Instr, Meth., B15, 435 (1986). J. H. Evans, Nucl. Instr, Meth,, B18, 16 (1986). G. W. Greenwood, A. J. E. Foreman and D. E. Rimmer, J. Nucl. Mater., 4, 305 (1959). J. H. Evans and D. J. Mazey, J. Nucl. M~ter,, 138, 176 (1986). E. M. Schulson, J. Nucl. Mater.. 83, 239 (1979). K. Y. Liou and P. Wilkes, I. Nucl. Mater., 87, 317 (1979). R. H. Zee and P. Wilkes, in Phase Stability Doring Irradiation, The Metallurgical Society of AIME, Warrendale (1981) p. 295. S. Banerjee and K" Urban, Phvs. Stat. Sol. (a), 81, 145 (1984). D. I. Potter, L. E. Rehn, P. R. Okamoto and H. Wiedersich, Scr. Metall., 1_!.1, 1095 (1977). S. M. Murphy, Phil. Mag. A, 58, No. 2, 417 (1988). J. R. Manning, Metall, Trans,, 1, 499 (1971). R. P. Gupta, Phvs._ Rev., B22, 5900 (1980). S. M. Murphy, in Proc. BNES Conf. on Materials for Nuclear Reactor Core Applications, Brighton, 1 (1987) p. 301. J. L. Brimhall, H. E. Kissinger and L. A. Chariot, Rad, Eft,, 77, 273 (1983). J. L. Brimhall and E. P. Simonen, Nucl. In~tr, Meth., BI6, 187 (1986). L. S. Hung, and J. W. Mayer, Nucl. Instr, Meth,, B7/8, 676 (1985). G. S. Was and J. M. Eridon, Nucl. Instr, Meth,, B24/25, 557 (1987). H. Wiedersich, in Radiation Damage in Metals, N. L. Peterson and S. D. Harkness, eds., American Society for Metals, Metals Park, OH (1976) p. 157. A. D. Brailsford and R. Bullough, J. Nucl. Mater,, 69&70, 434 (1978).

330

174.

175. 176. 177.

178. 179. 180.

181. 182. 183. 184.

185.

186.

187.

188. 189.

190. 191. 192. 193.

194.

195.

196.

197.

198. 199.

200. 201. 202.

203. 204.

G.S. WAS

D. I. Potter, in Phase Transformations During Irradiation, F. V. Nolfi, Jr., ed., Applied Science Publishers, New York (1983) p. 213. J. Eridon, L. Rehn and G. Was, Nucl, Instr. Meth,, B19/20, 626 (1987). D. E. Luzzi and M. Meshii, Scr. Metall., 20, 943 (1986). J. Koike, P. R. Okamoto, L. E. Rehn, P. Bhadra, M. H. Grimsditch and M. Meshii, Mat. Res. Soc. Symp., vol. (1989), paper All.3. E. Johnson, T. Wohlenberg and W. A. Grant, Phase Transitions, 1, 23 (1979). W. A. Grant, Nucl. Instr. Meth., 182/183, 809 (1981). E. Johnson, U. Littmark, A. Johnson and C. Christodoulides, phil. Mag. A, 45, 803 (1982). D. M. Follstaedt, Nucl. Instr, Meth., B7[8, 11 (1985). P. Ziemann, Mater, Sci. Engin,, 69, 95 (1985). J. Eridon, G. S. Was and L. Rehn, ,I. Mater. Res., 3, No. 4, 626 (1988). L. S. Hung, M. Nastasi, J. Gyulai and J. W. Mayer, Appl. Phys, Lett., 42, 622 (1983). M. Nastasi, L. S. Hung and J. W. Mayer, Appl. Phys. Lett., 43, No. 9, 831 (1983). D. A. Lilienfield, L. S. Hung and J. W. Mayer, Nucl. Instr. Meth., B 19/20, 1 (1987). D. A. Lilienfield and J. W. Mayer, Mat. Res. Soc. Symp. vol 74, Pittsburgh (1987) p. 339. B. X. Liu, Phys. St~t, Sol. (a), 94, 11 (1986). H. Jones in The Th¢ory Qf Brillouin Zone~ and Electronic States in Crystals, North-Holland, Amsterdam (1960) p. 191. B. X. Liu, Phvs. Stat. Sol. (a), 75, K77 (1983). B. Y. Tsaur, S. S. Lau and J. W. Mayer, Appl. Phvs. Lett., 36, 823 (1980). B. Y. Tsaur and J. W. Mayer, Appl. Phys. Lett., 37, 389 (1980). B. Y. Tsaur, S. S. Lau, L. S. Hung and J. W. Mayer, Nucl. Instr. Meth., 182/183, 67 (1981). J. W. Mayer, B. Y. Tsaur, S. S. Lau and L. S. Jung, Nucl. Instr. Meth., 182/183, 1 (1981). B. X. Liu, L. J. Huang, J. Li and E. Ma, in Thin Films - Interfaces and Phenomena, R. J. Nemanich, P. S. Ho and S. S. Lau, eds., Mat. Res. Soc. Symp. Proc., vol. 54, North-Holland, Amsterdam (1986) p. 217. B. X. Liu, E. MA, J. Li and L. J. Huang, Nucl. Instr. Meth., B 19•20, 682 (1987). J. Meissner, K. Kopitzki, G. Mertler and E. Peiner, Nucl. Instr. Meth., B19[20, 669 (1987). E. Peiner and K. Kopitzki, Nucl. Instr. M¢th,, B~4, 173 (1988). D. Shectman, I. Blech, D. Gratias and J. W. Chan, Phys. Rev. Lett., 53, 1951 (1984). P. J. Steinhardt, Amer, Sci,, 74, 586 (1986). J. A. Knapp and D. M. Follstaedt, Phys. Rev. Lett,, 55, No. 15, 1591 (1985). D. A. Lilienfield, M. Nastasi, H. H. Johnson, A. G. Ast and J. W. Mayer, phys. Rev. Lett., 55, No. 15, 1587 (1985). P. M. Ossi, Mater. Sci. Engin,, 90, 55 (1977). D. E. Luzzi, H. Moil, H. Fujita and M. Meshii, Scr, Metall., 18, 957 (1984).

205. 206. 207. 208. 209. 210. 211. 212. 213. 214

215.

216.

217.

218. 219.

220. 221. 222. 223.

224.

225. 226. 227.

228. 229. 230. 231.

232. 233. 234.

235. 236. 237.

238. 239.


D. F. Pedraza, Rad. Eft,, 112, 11 (1990). D. F. Pedraza, Mater. Sci. Engin., 90, 69 (1987). D. F. Pedraza and L. K. Mansur, Nucl. Instr. Meth., B16, 203 (1986). D. F. Pedraza, J. Mater. Res.. 1, 425 (1986). E. P. Simonen, NU¢I, Instr. Meth., B16, 198 (1986). G. H~igg, Z. Phvs. Chem. B, 12, 3 (1931).

331

B. Rauschenbach and K. Hohmuth, Phvs. Stat. Sol. (a), 7__2_2, 667 (1982). W. A. Grant, A. Ali and P. J. Grundy, Nucl. Instr. Meth.. 182/183, (1981). J. Hafner, Phvs. Rev.. B21, 406 (1980). R. Miedema, R. Boom and F. R. DeBoer, J. Less Comm. Metals, 4__!_1, 283 (1975). W. W. Hu, C. R. Clayton, H. Hermann, J. K. Hirvonen and R. A. Kant, Rad. Eft., 4__99, 71 (1980). K. Hohmuth, B. Rauschenbach, A. Kolitsch and E. Richter, Noel. Instr. Meth., 2091210, 249 (1983). R. Andrew, W. A. Grant, P. J. Grundy, J. S. Williams, and L. T. Chadderton, Nature, 262, 380 (1976). S. R. Nagel and J. Tauc, Phys. Rev. Lett., 35, 380 (1975). B. Rauschenbach and V. Heera, ..D~fect and Diffusion Data, 57-58, 143 (1988). H. M. Naguib and R. Kelly, Rad. Eft,, 25, 1 (1975). J. A. Alonso and S. Simozar, Solid State Corn.m,, 48, 765 (1983). A. R. Miedema, J. Less Comm, M~,,32, 117 (1973). B. X. Liu, W. L. Johnson, M-A. Nicolet and S. S. Lau, Nucl. Instr. Mater.. 209/210, 97 (1983). B. X. Liu, Wl. L. Johnson, M-A. Nicolet and S. S. Lau, Appl. Phys. Lett,, 4__22, No. 1, 45 (1983). G. Martin, Phv. Rev.. B30, 1424 (1984). M. L. Swanson, J. R. Parsons and C. W. Hoelke, Rad, Eft., 9, 249 (1971). J. L. Brimhall, E. P. Simonen and H. E. Kissinger, J, Nucl. Mater,, 48, 339 (1973). J. L. Brimhall and E. P. Simonen, Nocl, In~lr, Meth,, B16, 187 (1986). J. L. Brimhall, H. E. Kissinger and A. R. Pelton, Rad, Eft., 90, 241 (1985). E. P. Simonen, Nucl. Instr. Meth,, B16, |98 (1986). V. Goerlach, P. Ziemann and W. Buckel, N~lql. Instr. Meth., 209/210, 235 (1983). W. Folberth, H. Leitz and J. Hasse, Z. Phys., B43, 235 (1981). A. Schmid and P. Ziemann, N0¢I, Instr. Meth,, B718, 581 (1985). P. R. Okamoto, L. E. Rehn, J. Pearson, R. Bhadra and M. Grimsditch, in Mat. Res. Soc. Symp. Proc. vol. 100, MRS, Pittsburgh (1980) p. 51. W. L. Johnson, Pro~. Mater. Sci,, 30, 287 (1986). R. W. Cahn and W. L. Johnson, L Mater. Res,, l , 724 (1986). W. J. Meng, P. R. Okamoto, B. J. Kestel, L. J. Thompson and L. E. Rehn, A_,p.p.L Phys. Lett,, 53, 7 (1988). P. M. Ossi, Mater. $ci, Engin., A l l5 , 107 (1989). L. Thome, A. Benyagoub, F. Pons, E. Ligeon, J. Fontenille and R. Danielou, Mater. Sci. Engin., A1 !5, 127 (1989).

332

240. 241

242.

243.

244. 245.

246.

247. 248.

249. 250.

251.

252.

G.S. WAS

A. Benyagoub and L. Thome, Phvs. Rev. 1~, 38, No. 15, 10205 (1988). P. J. Martin, R. P. Netterfield and W. G. Sainty, J. Appl. Phys., 55, 235 (1984). R. P. Netterfield, W. G. Sainty, P. J. Martion and S. H. Sie, Appl. Opt., 24, 2267 (1985). F. A. Smidt, Proc. DOE Workshop on Coatings for Advanced Heat Engines, USDOE, 1988. J. C. Liu and J. W. Mayer, Nucl. Instr. Meth.. B19[20, 538 (1987). H. A. Atwater, C. V. Thompson and H. I. Smith, Mat. Res. Soc. Symp. Proc., vol. 100, MRS, Pittsburgh (1987) p. 345. D. E. Alexander, G. S. Was and L. E. Rehn, Mat. Res. Soc. Symp. Proc,, Fall 1989, paper A6.1. C. W. Allen and L. E. Rehn, Mat. Res. Soc. Symp. Proc., Fall 1989, paper A2.1. J. C. Liu, J. W. Mayer, C. W. Allen and L. E. Rehn, in Processing and Characterization 9f Materials U~ing I0n Beams, L. E Rehn, J. Greene and F. A. Smidt, eds., Materials Research Society, Pittsburgh, AP, 1988, Vol. 128, p. 297. M. Ahmed and D. I. Potter, Acta Metall., 35, No. 9, 2341 (1987). Z. Nishiyama, in Martensitic Transformations, M. E. Fine, M. Meshii and C. M. Wayman, eds., vol. 7, Academic Press, New York (1978). R. M. Bradley, J. M. E. Harper and D. A. Smith, ,I. Appl. Phys., 60, 4160 (1986). L. J. Huang, J. R. Ding, H-D. Li and B. X. Liu, Nucl, Instr. Meth., B39, 144 (1989).

ion beam modification of metals: compositional and microstructural

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